{"id":2322,"date":"2026-01-13T15:01:56","date_gmt":"2026-01-13T15:01:56","guid":{"rendered":"https:\/\/www.mathros.net.ua\/en\/?page_id=2322"},"modified":"2026-01-13T15:05:29","modified_gmt":"2026-01-13T15:05:29","slug":"inverse-of-a-matrix-calculator-by-gauss-jordan-method","status":"publish","type":"page","link":"https:\/\/www.mathros.net.ua\/en\/inverse-of-a-matrix-calculator-by-gauss-jordan-method","title":{"rendered":"Inverse of a Matrix Calculator: Step-by-Step Gauss\u2013Jordan Calculation"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"2322\" class=\"elementor elementor-2322\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0e7e4a8 e-flex e-con-boxed e-con e-parent\" data-id=\"0e7e4a8\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e60bd78 elementor-widget elementor-widget-html\" data-id=\"e60bd78\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"h2-title\">Checking Your Solution or Starting from Scratch? This Online Calculator Helps You Find the Inverse of a Matrix Accurately\u2014no Mistakes<\/h2>\n<style>\n    \/* h2 \u2014 \u0441\u0443\u0447\u0430\u0441\u043d\u0438\u0439, \u0447\u0438\u0442\u0430\u0431\u0435\u043b\u044c\u043d\u0438\u0439, \u0431\u0435\u0437 \u0440\u0430\u043c\u043e\u043a *\/\n.h2-title {\n  \/* \u0442\u0438\u043f\u043e\u0433\u0440\u0430\u0444\u0456\u043a\u0430 *\/\n  font-family: system-ui, -apple-system, \"Segoe UI\", Roboto, \"Helvetica Neue\", Arial, \"Noto Sans\", \"Liberation Sans\", sans-serif;\n  font-weight: 800;\n  font-size: clamp(1.2rem, 1rem + 1.2vw, 1.65rem); \/* ~19px\u201326px \u0430\u0434\u0430\u043f\u0442\u0438\u0432\u043d\u043e *\/\n  line-height: 1.3;\n  letter-spacing: .005em;\n\n  \/* \u043a\u043e\u043b\u0456\u0440 (\u043a\u0440\u0430\u0449\u0435 \u0437\u0430 \u00ab\u0441\u0456\u0440\u0438\u0439\u00bb \u0437 \u0442\u043e\u0447\u043a\u0438 \u0437\u043e\u0440\u0443 \u043a\u043e\u043d\u0442\u0440\u0430\u0441\u0442\u0443) *\/\n  color: #334155; \/* slate-700 *\/\n\n  \/* \u043c\u0430\u043a\u0435\u0442 \u0456 \u0447\u0438\u0442\u0430\u0431\u0435\u043b\u044c\u043d\u0456\u0441\u0442\u044c *\/\n  text-align: center;\n  max-width: 800px; 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}\n}\n<\/style>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ee08900 elementor-widget elementor-widget-html\" data-id=\"ee08900\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<!-- MathJax v2 (\u044f\u043a \u0443 \u0432\u0430\u0441) -->\r\n<script type=\"text\/javascript\" async\r\n  src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\">\r\n<\/script>\r\n\r\n<!-- ======================== HTML ======================== -->\r\n<div class=\"calculator-container inverse-ui\">\r\n  <div class=\"matrix-controls\">\r\n      <div class=\"matrix-controls__item\">\r\n          <label for=\"matrixSize\">Matrix dimensions<\/label>\r\n          <select id=\"matrixSize\" name=\"matrixSize\">\r\n            <option value=\"2\">2\u00d72<\/option>\r\n            <option value=\"3\" selected>3\u00d73<\/option>\r\n            <option value=\"4\">4\u00d74<\/option>\r\n            <option value=\"5\">5\u00d75<\/option>\r\n            <option value=\"6\">6\u00d76<\/option>\r\n            <option value=\"7\">7\u00d77<\/option>\r\n            <option value=\"8\">8\u00d78<\/option>\r\n          <\/select>\r\n      <\/div>\r\n      \r\n    <!-- Actions -->\r\n    <div class=\"matrix-controls__item matrix-controls__item--actions\">\r\n      <label class=\"sr-only\" for=\"fillRandomBtn\">Actions<\/label>\r\n      <div class=\"matrix-actions\">\r\n        <button id=\"clearMatrixBtn\" type=\"button\" class=\"btn-secondary\">Clear<\/button>\r\n        <button id=\"fillRandomBtn\" type=\"button\" class=\"btn-secondary\">Fill randomly<\/button>\r\n      <\/div>\r\n    <\/div>\r\n  <\/div>\r\n  \r\n  <!-- Random fill settings -->\r\n  <details class=\"random-settings\">\r\n    <summary>Random fill settings<\/summary>\r\n    <div class=\"random-settings__grid\">\r\n      <div class=\"random-settings__item\">\r\n        <label for=\"randMin\">Minimum<\/label>\r\n        <input id=\"randMin\" type=\"text\" value=\"-5\" inputmode=\"numeric\" \/>\r\n      <\/div>\r\n      <div class=\"random-settings__item\">\r\n        <label for=\"randMax\">Maximum<\/label>\r\n        <input id=\"randMax\" type=\"text\" value=\"5\" inputmode=\"numeric\" \/>\r\n      <\/div>\r\n      <div class=\"random-settings__item\">\r\n        <label for=\"randDecimals\">Decimal places<\/label>\r\n        <select id=\"randDecimals\">\r\n          <option value=\"0\" selected>0<\/option>\r\n          <option value=\"1\">1<\/option>\r\n          <option value=\"2\">2<\/option>\r\n          <option value=\"3\">3<\/option>\r\n        <\/select>\r\n      <\/div>\r\n    <\/div>\r\n  <\/details>\r\n\r\n  <table id=\"matrixTable\" aria-label=\"Matrix input grid\"><\/table>\r\n\r\n  <button id=\"generate-button\" type=\"button\">Find the inverse of a matrix<\/button>\r\n<\/div>\r\n\r\n<div id=\"fcontainer\" class=\"solution-container\" style=\"display:none;\"><\/div>\r\n<div id=\"error-block\" class=\"error-message\" role=\"alert\" aria-live=\"polite\"><\/div>\r\n<div id=\"loading\" class=\"loader\" style=\"display:none;\"><\/div>\r\n\r\n\r\n<!-- ======================== CSS ========================= -->\r\n<style>\r\n\/* =========================================================\r\n   Modern, responsive UI for the calculator interface\r\n   Targets ONLY the provided markup:\r\n   .calculator-container, label, select, table#matrixTable, inputs in table,\r\n   #generate-button, #loading.loader, #error-block.error-message\r\n   - Desktop content width: 800px (centered)\r\n   - Clean focus states + dark mode\r\n   - Touch-friendly sizes, better spacing, subtle shadows\r\n   ========================================================= *\/\r\n\r\n\/* ---------- Design Tokens ---------- *\/\r\n:root{\r\n  --ui-bg:            #ffffff;\r\n  --ui-panel:         #f6f9fc;\r\n  --ui-border:        #e2e8f0;\r\n  --ui-text:          #0b2239;\r\n  --ui-text-muted:    #64748b;\r\n  --ui-accent:        #0b638b;\r\n  --ui-accent-weak:   rgba(11,99,139,.12);\r\n  --ui-danger:        #c0392b;\r\n  --ui-radius:        14px;\r\n  --ui-shadow:        0 8px 28px rgba(2, 8, 23, .06);\r\n  --ui-focus:         0 0 0 3px rgba(11, 99, 139, .22);\r\n  --ui-font:          system-ui, -apple-system, \"Segoe UI\", Roboto, \"Helvetica Neue\", Arial, \"Noto Sans\", \"Liberation Sans\", sans-serif;\r\n  --ui-cell-w:        110px;      \/* width of matrix inputs on desktop *\/\r\n  --ui-input-h:       44px;       \/* control height *\/\r\n  --ui-gap:           10px;       \/* spacing inside form grid *\/\r\n}\r\n\r\n@media (prefers-color-scheme: dark){\r\n  :root{\r\n    --ui-bg:          #0f1a22;\r\n    --ui-panel:       #13202a;\r\n    --ui-border:      #223142;\r\n    --ui-text:        #e6f1f7;\r\n    --ui-text-muted:  #9fb4c6;\r\n    --ui-accent:      #5ac2f2;\r\n    --ui-accent-weak: rgba(90,194,242,.18);\r\n    --ui-danger:      #ff7f7f;\r\n    --ui-shadow:      0 12px 36px rgba(0,0,0,.45);\r\n  }\r\n}\r\n\r\n\/* ---------- Calculator container ---------- *\/\r\n.calculator-container{\r\n  width: 800px;\r\n  max-width: 800px;\r\n  margin: 18px auto;\r\n  padding: 20px 20px 22px;\r\n  background: var(--ui-bg);\r\n  color: var(--ui-text);\r\n  border: 1px solid var(--ui-border);\r\n  border-radius: var(--ui-radius);\r\n  box-shadow: var(--ui-shadow);\r\n  font-family: var(--ui-font);\r\n}\r\n\r\n\/* ---------- Controls: label + select ---------- *\/\r\n.calculator-container label{\r\n  display:block;\r\n  font-weight:700;\r\n  font-size:.98rem;\r\n  letter-spacing:.01em;\r\n  margin: 0 0 8px 2px;\r\n  color: var(--ui-text);\r\n}\r\n\r\n.calculator-container select{\r\n  width: 220px;\r\n  height: var(--ui-input-h);\r\n  padding: 0 12px;\r\n  border-radius: 12px;\r\n  border: 1px solid var(--ui-border);\r\n  background: var(--ui-panel);\r\n  color: var(--ui-text);\r\n  font-weight: 600;\r\n  outline: none;\r\n  transition: box-shadow .15s ease, border-color .15s ease, background-color .2s ease, transform .05s ease;\r\n}\r\n.calculator-container select:hover{\r\n  border-color: var(--ui-accent);\r\n  background: color-mix(in oklab, var(--ui-panel), var(--ui-accent) 6%);\r\n}\r\n.calculator-container select:focus-visible{\r\n  border-color: var(--ui-accent);\r\n  box-shadow: var(--ui-focus);\r\n  background: #fff;\r\n  transform: translateY(-1px);\r\n}\r\n\r\n\/* ---------- Matrix table ---------- *\/\r\n.calculator-container table#matrixTable{\r\n  margin: 16px 0 12px;\r\n  border-left: 1px solid #ddd; \r\n  border-right: 1px solid #ddd;\r\n  border-collapse: collapse;\r\n  width: 100%;\r\n}\r\n.calculator-container table#matrixTable td, \r\n.calculator-container table#matrixTable th,\r\n.calculator-container table#matrixTable tr{\r\n  padding: 3px 3px;\r\n  margin: 0;\r\n  border: 0;\r\n}\r\n\r\n\/* ---------- Matrix inputs ---------- *\/\r\n.calculator-container table#matrixTable input[type=\"text\"]{\r\n  width: 100%;\r\n  max-width: 100%;\r\n  height: var(--ui-input-h);\r\n  box-sizing: border-box;\r\n  padding: 0 10px;\r\n  border: 1px solid var(--ui-border);\r\n  border-radius: 10px;\r\n  background: var(--ui-panel);\r\n  color: var(--ui-text);\r\n  font-weight: 600;\r\n  text-align: center;\r\n  transition: box-shadow .15s ease, border-color .15s ease, background-color .2s ease, transform .05s ease;\r\n  outline: none;\r\n}\r\n.calculator-container table#matrixTable input[type=\"text\"]::placeholder{\r\n  color: var(--ui-text-muted);\r\n  opacity: .75;\r\n}\r\n.calculator-container table#matrixTable input[type=\"text\"]:hover{\r\n  border-color: var(--ui-accent);\r\n  background: color-mix(in oklab, var(--ui-panel), var(--ui-accent) 6%);\r\n}\r\n.calculator-container table#matrixTable input[type=\"text\"]:focus-visible{\r\n  border-color: var(--ui-accent);\r\n  box-shadow: var(--ui-focus);\r\n  background: #fff;\r\n  transform: translateY(-1px);\r\n}\r\n\/* invalid state (if you add validation classes) *\/\r\n.calculator-container table#matrixTable input[type=\"text\"].is-error{\r\n  border-color: var(--ui-danger);\r\n  box-shadow: 0 0 0 2px color-mix(in oklab, var(--ui-danger), white 76%);\r\n}\r\n\r\n.calculator-container table#matrixTable input.input-error{\r\n  outline: 2px solid #d93025;\r\n  border-color: #d93025;\r\n}\r\n\r\n\/* ---------- Solve button ---------- *\/\r\n#generate-button,\r\n.calculator-container input[type=\"button\"]#generate-button{\r\n  display:inline-flex;\r\n  align-items:center;\r\n  justify-content:center;\r\n  gap:8px;\r\n\r\n  width:100%;\r\n  height:48px;\r\n  margin-top:10px;\r\n\r\n  background: var(--ui-accent);\r\n  color:#fff;\r\n  border:1px solid transparent;\r\n  border-radius: 12px;\r\n  font-weight: 800;\r\n  letter-spacing:.02em;\r\n  cursor:pointer;\r\n  transition: transform .05s ease, filter .15s ease, box-shadow .15s ease, background-color .2s ease;\r\n}\r\n#generate-button:hover{\r\n  filter: brightness(1.05);\r\n  box-shadow: 0 10px 30px rgba(11,99,139,.18);\r\n}\r\n#generate-button:active{\r\n  transform: translateY(1px);\r\n}\r\n#generate-button:disabled{\r\n  opacity:.55;\r\n  cursor:not-allowed;\r\n  box-shadow:none;\r\n}\r\n\r\n\/* ---------- Loader ---------- *\/\r\n.loader{\r\n  margin: 20px auto;\r\n  border: 6px solid #e9eef5;\r\n  border-top: 6px solid var(--ui-accent);\r\n  border-radius: 50%;\r\n  width: 75px; height: 75px;\r\n  animation: spin .9s linear infinite;\r\n}\r\n@keyframes spin{ to{ transform: rotate(360deg); } }\r\n\r\n\/* ---------- Error message ---------- *\/\r\n.error-message{\r\n  display:none; \/* toggled with .show *\/\r\n  width: 800px;\r\n  max-width: 800px;\r\n  margin: 14px auto 0;\r\n  background: color-mix(in oklab, var(--ui-danger), white 90%);\r\n  color: var(--ui-danger);\r\n  border: 1px solid color-mix(in oklab, var(--ui-danger), white 68%);\r\n  border-left: 4px solid var(--ui-danger);\r\n  border-radius: 12px;\r\n  padding: 12px 14px;\r\n  box-shadow: var(--ui-shadow);\r\n  font-weight: 600;\r\n  font-family: var(--ui-font);\r\n}\r\n.error-message.show{ display:block; animation: fadeIn .4s ease-in-out; }\r\n@keyframes fadeIn{ from{opacity:0} to{opacity:1} }\r\n\r\n\/* ---------- Global focus-visible helper ---------- *\/\r\n:focus-visible{\r\n  outline: none;\r\n  box-shadow: var(--ui-focus);\r\n}\r\n\r\n\/* =========================================================\r\n   Responsive adaptations\r\n   - Keep a polished look on tablets\/phones\r\n   ========================================================= *\/\r\n\r\n\/* Tablets (<= 1024px): relax fixed width, keep proportions *\/\r\n@media (max-width:1024px){\r\n  .calculator-container,\r\n  .error-message{\r\n    width: min(800px, calc(100% - 48px));\r\n    max-width: 100%;\r\n    margin-left: auto;\r\n    margin-right: auto;\r\n  }\r\n\r\n  .calculator-container select{\r\n    width: 260px; \/* a bit wider for finger comfort *\/\r\n  }\r\n\r\n  .calculator-container table#matrixTable{\r\n    border-spacing: 8px;\r\n  }\r\n  .calculator-container table#matrixTable input[type=\"text\"]{\r\n    width: 100px; \/* slightly narrower to fit *\/\r\n  }\r\n}\r\n\r\n\/* Mobile landscape \/ small tablets (<= 860px) *\/\r\n@media (max-width:860px){\r\n  .calculator-container,\r\n  .error-message{\r\n    width: calc(100% - 32px);\r\n    margin-left:16px; margin-right:16px;\r\n    padding: 18px;\r\n  }\r\n  .calculator-container select{ width: 220px; }\r\n  .calculator-container table#matrixTable input[type=\"text\"]{\r\n    width: 90px; height: 42px; font-size: .98rem;\r\n  }\r\n  #generate-button{ height: 46px; }\r\n}\r\n\r\n\/* Phones (<= 768px): stack tightly, keep tap sizes *\/\r\n@media (max-width:768px){\r\n  :root{ --ui-gap: 8px; --ui-cell-w: 84px; }\r\n\r\n  .calculator-container{ padding:16px; }\r\n  .calculator-container label{ font-size:.95rem; margin-bottom:6px; }\r\n\r\n  .calculator-container select{\r\n    width: 100%;\r\n    height: 44px;\r\n  }\r\n\r\n  .calculator-container table#matrixTable{\r\n    border-spacing: 6px;\r\n  }\r\n  .calculator-container table#matrixTable input[type=\"text\"]{\r\n    width: var(--ui-cell-w);\r\n    height: 42px;\r\n    font-size: .96rem;\r\n    padding: 0 8px;\r\n  }\r\n\r\n  #generate-button{ height: 46px; font-size: 1rem; }\r\n  .error-message{ width: calc(100% - 32px); max-width: none; }\r\n}\r\n\r\n\/* Extra small phones (<= 480px): compact grid cells *\/\r\n@media (max-width:480px){\r\n  :root{ --ui-cell-w: 76px; }\r\n\r\n  .calculator-container{\r\n    padding: 14px;\r\n  }\r\n  .calculator-container table#matrixTable{\r\n    border-spacing: 6px;\r\n  }\r\n  .calculator-container table#matrixTable input[type=\"text\"]{\r\n    width: var(--ui-cell-w);\r\n    height: 40px;\r\n    font-size: .95rem;\r\n  }\r\n}\r\n\r\n\/* =========================================================\r\n   Optional: prefers-reduced-motion\r\n   ========================================================= *\/\r\n@media (prefers-reduced-motion: reduce){\r\n  *{ animation-duration: .01ms !important; animation-iteration-count: 1 !important; transition-duration: .01ms !important; scroll-behavior: auto !important; }\r\n}\r\n\r\n\r\n\r\n\r\n\/* === \u041f\u041e\u0412\u041d\u0418\u0419 CSS \u0414\u041b\u042f \u0412\u0418\u0412\u0415\u0414\u0415\u041d\u041d\u042f \u0426\u0406\u041b\u041e\u0413\u041e \u0420\u0406\u0428\u0415\u041d\u041d\u042f (\u041c\u0435\u0442\u043e\u0434 \u041a\u0440\u0430\u043c\u0435\u0440\u0430) ===\r\n   \u0426\u0456\u043b\u0456:\r\n   1) \u0410\u043a\u0443\u0440\u0430\u0442\u043d\u0456 \u043a\u0430\u0440\u0442\u043a\u0438-\u043a\u0440\u043e\u043a\u0438 \u0443 \u0442\u0430\u0439\u043c\u043b\u0430\u0439\u043d\u0456.\r\n   2) \u0416\u043e\u0434\u0435\u043d .cramer-step \u043d\u0435 \u0432\u0438\u0445\u043e\u0434\u0438\u0442\u044c \u0437\u0430 \u043c\u0435\u0436\u0456 .solution-container.\r\n   3) \u0424\u043e\u0440\u043c\u0443\u043b\u0438 (MathJax\/KaTeX) \u043c\u0430\u044e\u0442\u044c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0443 \u043f\u0440\u043e\u043a\u0440\u0443\u0442\u043a\u0443 \u0437\u0430\u043c\u0456\u0441\u0442\u044c \u043f\u0435\u0440\u0435\u043f\u043e\u0432\u043d\u0435\u043d\u043d\u044f.\r\n*\/\r\n\r\n\/* ===================== \u0411\u0410\u0417\u041e\u0412\u0406 \u0421\u0422\u0418\u041b\u0406 (\u0434\u0435\u0441\u043a\u0442\u043e\u043f, 800px) ===================== *\/\r\n\/* \u041f\u0430\u043b\u0456\u0442\u0440\u0430 (\u0441\u0432\u0456\u0442\u043b\u0430\/\u0442\u0435\u043c\u043d\u0430 \u0442\u0435\u043c\u0430) *\/\r\n:root {\r\n  --cs-bg:            #f7fbff;\r\n  --cs-card:          #ffffff;\r\n  --cs-border:        #d6e7f8;\r\n  --cs-text:          #0b2239;\r\n  --cs-muted:         #5c7286;\r\n  --cs-accent:        #0b638b; \/* Primary blue *\/\r\n  --cs-accent-weak:   rgba(11, 99, 139, 0.12);\r\n  --cs-success:       #107a3c;\r\n  --cs-warn:          #8a5b00;\r\n  --cs-error:         #9b2424;\r\n  --cs-shadow:        0 6px 24px rgba(11, 99, 139, 0.08);\r\n}\r\n\r\n@media (prefers-color-scheme: dark) {\r\n  :root {\r\n    --cs-bg:          #0f1a22;\r\n    --cs-card:        #16232c;\r\n    --cs-border:      #203241;\r\n    --cs-text:        #e6f1f7;\r\n    --cs-muted:       #9eb6c7;\r\n    --cs-accent:      #5ac2f2;\r\n    --cs-accent-weak: rgba(90, 194, 242, 0.16);\r\n    --cs-success:     #4cd17d;\r\n    --cs-warn:        #ffc156;\r\n    --cs-error:       #ff7b7b;\r\n    --cs-shadow:      0 10px 36px rgba(0, 0, 0, 0.35);\r\n  }\r\n}\r\n\r\n\/* \u0424\u0456\u043a\u0441\u043e\u0432\u0430\u043d\u0438\u0439 \u043a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 (\u0414\u0415\u0421\u041a\u0422\u041e\u041f): 800px, \u0431\u0435\u0437 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0441\u043a\u0440\u043e\u043b\u0443 *\/\r\n.solution-container {\r\n  width: 100%;\/*800px;*\/\r\n  max-width: 100%;\/*800px;*\/\r\n  min-width: 100%;\/*800px;*\/\r\n  margin: 15px auto;\r\n  padding: 20px;\r\n\r\n  background: #fff;\r\n  color: #333;\r\n  font: 16px\/1.6 system-ui, -apple-system, \"Segoe UI\", Roboto, \"Helvetica Neue\", Arial, \"Noto Sans\", \"Liberation Sans\", sans-serif;\r\n\r\n  overflow-x: hidden; \/* \u043a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 \u043d\u0435 \u0441\u043a\u0440\u043e\u043b\u0438\u0442\u044c\u0441\u044f \u043f\u043e \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u0456 *\/\r\n  overflow-y: visible;\r\n}\r\n\r\n\/* \u041e\u0431\u0433\u043e\u0440\u0442\u043a\u0430 \u043a\u0440\u043e\u043a\u0456\u0432 *\/\r\n.solution-container .cramer-solution {\r\n  counter-reset: step;\r\n  display: grid;\r\n  gap: 14px;\r\n  margin-top: 8px;\r\n}\r\n\r\n\/* \u0417\u0430\u0433\u043e\u043b\u043e\u0432\u043e\u043a \u0440\u0456\u0448\u0435\u043d\u043d\u044f *\/\r\n.solution-container .cramer-heading{\r\n  display:flex;\r\n  flex-direction:column;\r\n  gap:6px;\r\n  margin: 4px 0 12px;\r\n  padding: 14px 16px;\r\n  \/*border:1px solid var(--cs-border, #d6e7f8);\r\n  border-radius: 14px;\r\n  background: var(--cs-bg, #f7fbff);\r\n  box-shadow: var(--cs-shadow, 0 6px 24px rgba(11,99,139,.08));*\/\r\n}\r\n\r\n.solution-container .cramer-heading__title{\r\n  font-weight: 800;\r\n  font-size: clamp(1.1rem, 1rem + 0.5vw, 1.35rem);\r\n  letter-spacing: .01em;\r\n  color: var(--cs-text, #0b2239);\r\n}\r\n\r\n.solution-container .cramer-heading__meta{\r\n  font-size: .88rem;\r\n  color: var(--cs-muted, #5c7286);\r\n}\r\n\r\n\/* \u0422\u0435\u043c\u043d\u0430 \u0442\u0435\u043c\u0430 \u0437 \u0432\u0430\u0448\u0438\u043c\u0438 \u0442\u043e\u043a\u0435\u043d\u0430\u043c\u0438 *\/\r\n@media (prefers-color-scheme: dark){\r\n  .solution-container .cramer-heading{\r\n    border-color: var(--cs-border, #203241);\r\n    background: var(--cs-card, #16232c);\r\n    box-shadow: var(--cs-shadow, 0 10px 36px rgba(0,0,0,.35));\r\n  }\r\n  .solution-container .cramer-heading__meta{\r\n    color: var(--cs-muted, #9eb6c7);\r\n  }\r\n}\r\n\r\n\/* \u0410\u0434\u0430\u043f\u0442\u0430\u0446\u0456\u044f *\/\r\n@media (max-width: 768px){\r\n  .solution-container .cramer-heading{\r\n    padding: 12px 12px;\r\n    border-radius: 12px;\r\n  }\r\n}\r\n\r\n\r\n\/* \u041a\u0430\u0440\u0442\u043a\u0430 \u043a\u0440\u043e\u043a\u0443 *\/\r\n.solution-container .cramer-step {\r\n  position: relative;\r\n  min-width: 0; \/* \u0434\u043e\u0437\u0432\u043e\u043b\u044f\u0454 \u0432\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0456\u043c \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c \u043a\u0435\u0440\u0443\u0432\u0430\u0442\u0438 \u0441\u0432\u043e\u0457\u043c \u0441\u043a\u0440\u043e\u043b\u043e\u043c *\/\r\n  padding: 16px 16px 16px 60px;\r\n  background: var(--cs-card);\r\n  border: 1px solid var(--cs-border);\r\n  border-radius: 14px;\r\n  box-shadow: var(--cs-shadow);\r\n  color: var(--cs-text);\r\n  line-height: 1.6;\r\n}\r\n\r\n\/* \u041d\u043e\u043c\u0435\u0440 \u043a\u0440\u043e\u043a\u0443 \u0432 \u043a\u0440\u0443\u0436\u0435\u0447\u043a\u0443 *\/\r\n.solution-container .cramer-step::before {\r\n  content: counter(step);\r\n  counter-increment: step;\r\n  position: absolute;\r\n  top: 16px;\r\n  left: 16px;\r\n  width: 28px;\r\n  height: 28px;\r\n  display: grid;\r\n  place-items: center;\r\n  border-radius: 999px;\r\n  background: var(--cs-accent-weak);\r\n  border: 1px solid var(--cs-border);\r\n  color: var(--cs-accent);\r\n  font: 700 0.95rem\/1 system-ui, -apple-system, \"Segoe UI\", Roboto, Arial, sans-serif;\r\n}\r\n\r\n\/* \u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430 \u043b\u0456\u043d\u0456\u044f-\u0442\u0430\u0439\u043c\u043b\u0430\u0439\u043d *\/\r\n.solution-container .cramer-step::after {\r\n  content: \"\";\r\n  position: absolute;\r\n  left: 30px;\r\n  top: 48px;\r\n  bottom: -14px;\r\n  width: 2px;\r\n  background: linear-gradient(to bottom, var(--cs-accent-weak), transparent 70%);\r\n}\r\n.solution-container .cramer-step:last-child::after { display: none; }\r\n\r\n\/* \u0417\u0430\u0433\u043e\u043b\u043e\u0432\u043e\u043a \u043a\u0440\u043e\u043a\u0443 *\/\r\n.solution-container .cramer-step__title,\r\n.solution-container .cramer-step > h3 {\r\n  margin: 0 0 8px 0;\r\n  font-weight: 700;\r\n  font-size: clamp(1.02rem, 0.95rem + 0.3vw, 1.15rem);\r\n  letter-spacing: .01em;\r\n}\r\n\r\n\/* \u0422\u0435\u043a\u0441\u0442 *\/\r\n.solution-container .cramer-step p {\r\n  margin: 0 0 8px 0;\r\n  color: var(--cs-text);\r\n}\r\n\r\n\/* \u0424\u043e\u0440\u043c\u0443\u043b\u0430: \u0454\u0434\u0438\u043d\u0435 \u043c\u0456\u0441\u0446\u0435, \u0434\u0435 \u0434\u043e\u043f\u0443\u0441\u043a\u0430\u0454\u0442\u044c\u0441\u044f \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0438\u0439 \u0441\u043a\u0440\u043e\u043b *\/\r\n.solution-container .cramer-step .formula {\r\n  background: #fff;\r\n  border: 1px dashed var(--cs-border);\r\n  border-left: 3px solid var(--cs-accent);\r\n  border-radius: 10px;\r\n  padding: 10px 12px;\r\n  margin-top: 8px;\r\n  \/* font-size: .78rem; *\/\r\n  max-width: 100%;\r\n  min-width: 0;\r\n  overflow-x: auto;    \/* \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430 \u043f\u043e\u043b\u043e\u0441\u0430 \u0441\u043a\u0440\u043e\u043b\u0443 \u043f\u0440\u0438 \u043f\u043e\u0442\u0440\u0435\u0431\u0456 *\/\r\n  overflow-y: hidden;\r\n  white-space: nowrap; \/* \u043d\u0435 \u043f\u0435\u0440\u0435\u043d\u043e\u0441\u0438\u0442\u0438 \u0434\u043e\u0432\u0433\u0456 \u0444\u043e\u0440\u043c\u0443\u043b\u0438 *\/\r\n  -webkit-overflow-scrolling: touch;\r\n\r\n  scrollbar-width: thin;                         \/* Firefox *\/\r\n  scrollbar-color: var(--cs-accent) transparent; \/* Firefox *\/\r\n}\r\n\r\n@media (prefers-color-scheme: dark) {\r\n  .solution-container .cramer-step .formula { background: #0f1a22; }\r\n}\r\n\r\n\/* MathJax\/KaTeX \u2014 \u043d\u0435 \u043b\u0430\u043c\u0430\u0442\u0438 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0438\u0439 \u0441\u043a\u0440\u043e\u043b *\/\r\n.solution-container .cramer-step .formula .mjx-container,\r\n.solution-container .cramer-step .formula .katex-display,\r\n.solution-container .cramer-step .formula .katex {\r\n  display: inline-block !important;\r\n  white-space: nowrap !important;\r\n  max-width: none !important;\r\n}\r\n\r\n\/* \u041a\u0430\u0441\u0442\u043e\u043c\u043d\u0456 \u0441\u043a\u0440\u043e\u043b-\u0431\u0430\u0440\u0438 \u0434\u043b\u044f WebKit *\/\r\n.solution-container .cramer-step .formula::-webkit-scrollbar { height: 8px; }\r\n.solution-container .cramer-step .formula::-webkit-scrollbar-track { background: transparent; }\r\n.solution-container .cramer-step .formula::-webkit-scrollbar-thumb {\r\n  background-color: var(--cs-accent);\r\n  border-radius: 8px;\r\n  background-clip: padding-box;\r\n}\r\n.solution-container .cramer-step .formula::-webkit-scrollbar-thumb:hover { filter: brightness(0.9); }\r\n\r\n\/* \u0411\u0435\u0439\u0434\u0436\u0456 *\/\r\n.solution-container .cramer-badges {\r\n  display: flex;\r\n  flex-wrap: wrap;\r\n  gap: 8px;\r\n  margin: 6px 0 4px 0;\r\n}\r\n.solution-container .cramer-badge {\r\n  display: inline-flex;\r\n  align-items: center;\r\n  gap: 6px;\r\n  border-radius: 999px;\r\n  padding: 4px 10px;\r\n  font-weight: 700;\r\n  font-size: .78rem;\r\n  letter-spacing: .02em;\r\n  border: 1px solid var(--cs-border);\r\n  background: var(--cs-accent-weak);\r\n  color: var(--cs-accent);\r\n}\r\n.solution-container .cramer-badge--ok {\r\n  background: rgba(16, 122, 60, 0.12);\r\n  color: var(--cs-success);\r\n  border-color: rgba(16, 122, 60, 0.22);\r\n}\r\n\r\n\/* \u0414\u0435\u0442\u0430\u043b\u0456\/\u0441\u043f\u043e\u0439\u043b\u0435\u0440\u0438 *\/\r\n.solution-container .cramer-details { margin-top: 8px; }\r\n.solution-container .cramer-details > summary {\r\n  cursor: pointer;\r\n  list-style: none;\r\n  padding: 8px 12px;\r\n  border-radius: 10px;\r\n  border: 1px solid var(--cs-border);\r\n  background: var(--cs-bg);\r\n  color: var(--cs-text);\r\n  font-weight: 600;\r\n  transition: background-color .2s ease, border-color .2s ease;\r\n}\r\n.solution-container .cramer-details > summary::marker { content: \"\"; }\r\n.solution-container .cramer-details > summary::before {\r\n  content: \"\u25b8\";\r\n  display: inline-block;\r\n  margin-right: 8px;\r\n  transition: transform .2s ease;\r\n}\r\n.solution-container .cramer-details[open] > summary::before { transform: rotate(90deg); }\r\n\r\n\/* \u0412\u0438\u0434\u0456\u043b\u0435\u043d\u0438\u0439 \u043f\u0456\u0434\u0441\u0443\u043c\u043a\u043e\u0432\u0438\u0439 \u043a\u0440\u043e\u043a *\/\r\n.solution-container .cramer-step--result { border-left: 4px solid var(--cs-success); }\r\n.solution-container .cramer-step--result::before {\r\n  color: var(--cs-success);\r\n  background: rgba(16, 122, 60, 0.12);\r\n}\r\n\r\n\/* \u041f\u0456\u0434\u0441\u0432\u0456\u0442\u043a\u0438 *\/\r\n.solution-container .cramer-step em,\r\n.solution-container .cramer-step .highlight {\r\n  padding: 0.05rem 0.25rem;\r\n  border-radius: 6px;\r\n  background: var(--cs-accent-weak);\r\n  font-weight: 700;\r\n}\r\n\r\n\/* ===================== \u0410\u0414\u0410\u041f\u0422\u0410\u0426\u0406\u042f: \u041f\u041b\u0410\u041d\u0428\u0415\u0422\u0418 (<= 1024px) ===================== *\/\r\n@media (max-width: 1024px) {\r\n  .solution-container {\r\n    width: min(800px, calc(100% - 40px));\r\n    max-width: 100%;\r\n    min-width: 0;          \/* \u0437\u043d\u044f\u0442\u0438 \u0436\u043e\u0440\u0441\u0442\u043a\u0435 \u043e\u0431\u043c\u0435\u0436\u0435\u043d\u043d\u044f *\/\r\n    margin: 16px auto;\r\n    padding: 18px;\r\n    font-size: 15px;       \/* \u0442\u0440\u043e\u0445\u0438 \u043c\u0435\u043d\u0448\u0438\u0439 \u0431\u0430\u0437\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 *\/\r\n  }\r\n\r\n  .solution-container .cramer-step {\r\n    padding: 14px 14px 14px 56px;\r\n    border-radius: 12px;\r\n  }\r\n\r\n  .solution-container .cramer-step::before {\r\n    width: 26px; height: 26px;\r\n    font-size: 0.9rem;\r\n    top: 14px; left: 14px;\r\n  }\r\n  .solution-container .cramer-step::after { left: 28px; top: 44px; }\r\n\r\n  .solution-container .cramer-step .formula {\r\n    padding: 9px 10px;\r\n    font-size: 0.98em;\r\n  }\r\n\r\n  .solution-container .cramer-badge { font-size: .76rem; }\r\n}\r\n\r\n\/* ===================== \u0410\u0414\u0410\u041f\u0422\u0410\u0426\u0406\u042f: \u041c\u041e\u0411\u0406\u041b\u042c\u041d\u0406 (<= 768px) ===================== *\/\r\n@media (max-width: 768px) {\r\n  .solution-container {\r\n    width: calc(100% - 24px);\r\n    max-width: 100%;\r\n    min-width: 0;\r\n    margin: 12px auto;\r\n    padding: 14px;\r\n    font-size: 14px;\r\n  }\r\n\r\n  .solution-container .cramer-solution { gap: 12px; }\r\n\r\n  .solution-container .cramer-step {\r\n    padding: 12px 12px 12px 52px;\r\n    border-radius: 12px;\r\n  }\r\n\r\n  \/* \u0417\u043c\u0435\u043d\u0448\u0438\u0442\u0438\/\u0441\u043f\u0440\u043e\u0441\u0442\u0438\u0442\u0438 \u043c\u0430\u0440\u043a\u0435\u0440\u0438 \u043a\u0440\u043e\u043a\u0456\u0432 \u0456 \u0442\u0430\u0439\u043c\u043b\u0430\u0439\u043d *\/\r\n  .solution-container .cramer-step::before {\r\n    width: 24px; height: 24px;\r\n    font-size: 0.85rem;\r\n    top: 12px; left: 12px;\r\n  }\r\n  .solution-container .cramer-step::after {\r\n    left: 26px;\r\n    top: 40px;\r\n    bottom: -12px;\r\n  }\r\n\r\n  .solution-container .cramer-step__title,\r\n  .solution-container .cramer-step > h3 {\r\n    font-size: 1rem; \/* \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u0456\u0448\u0435 \u043d\u0430 \u043c\u043e\u0431\u0456\u043b\u044c\u043d\u043e\u043c\u0443 *\/\r\n    margin-bottom: 6px;\r\n  }\r\n\r\n  .solution-container .cramer-step p { margin-bottom: 6px; }\r\n\r\n  .solution-container .cramer-step .formula {\r\n    padding: 8px 10px;\r\n    font-size: 0.96em; \/* \u0442\u0440\u0456\u0448\u043a\u0438 \u0437\u043c\u0435\u043d\u0448\u0438\u0442\u0438 \u0449\u0456\u043b\u044c\u043d\u0456\u0441\u0442\u044c *\/\r\n  }\r\n\r\n  \/* \u0417\u043c\u0435\u043d\u0448\u0435\u043d\u0456 \u0431\u0435\u0439\u0434\u0436\u0456 *\/\r\n  .solution-container .cramer-badge {\r\n    padding: 3px 8px;\r\n    font-size: .74rem;\r\n    border-radius: 999px;\r\n  }\r\n\r\n  \/* \u0429\u043e\u0431 \u0434\u0440\u0456\u0431\u043d\u0456 \u0435\u043a\u0440\u0430\u043d\u0438 \u043d\u0435 \u043e\u0442\u0440\u0438\u043c\u0443\u0432\u0430\u043b\u0438 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0438\u0439 \u201c\u0448\u0442\u0438\u0440\u201d \u0442\u0430\u0439\u043c\u043b\u0430\u0439\u043d\u0443 \u0434\u0443\u0436\u0435 \u0434\u043e\u0432\u0433\u0438\u043c *\/\r\n  .solution-container .cramer-step:last-child::after { display: none; }\r\n}\r\n\r\n\/* ========== \u0414\u0423\u0416\u0415 \u041c\u0410\u041b\u0406 \u041c\u041e\u0411\u0406\u041b\u042c\u041d\u0406 (<= 480px): \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u043e ========== *\/\r\n@media (max-width: 480px) {\r\n  .solution-container {\r\n    width: calc(100% - 16px);\r\n    margin: 10px auto;\r\n    padding: 12px;\r\n    font-size: 13.5px;\r\n  }\r\n\r\n  .solution-container .cramer-step {\r\n    padding: 10px 10px 10px 46px;\r\n    border-radius: 10px;\r\n  }\r\n\r\n  .solution-container .cramer-step::before {\r\n    width: 22px; height: 22px;\r\n    font-size: 0.8rem;\r\n    top: 10px; left: 10px;\r\n  }\r\n  .solution-container .cramer-step::after { display: none; } \/* \u043f\u0440\u0438\u0431\u0440\u0430\u0442\u0438 \u043b\u0456\u043d\u0456\u044e \u0434\u043b\u044f \u043f\u043e\u0432\u0456\u0442\u0440\u044f *\/\r\n\r\n  .solution-container .cramer-step__title,\r\n  .solution-container .cramer-step > h3 {\r\n    font-size: .98rem;\r\n    margin-bottom: 4px;\r\n  }\r\n\r\n  .solution-container .cramer-step .formula {\r\n    padding: 6px 8px;\r\n    font-size: 0.94em;\r\n    \/* \u0437\u0430\u043b\u0438\u0448\u0430\u0454\u043c\u043e \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0438\u0439 \u0441\u043a\u0440\u043e\u043b \u0434\u043b\u044f \u0434\u043e\u0432\u0433\u0438\u0445 \u0444\u043e\u0440\u043c\u0443\u043b *\/\r\n  }\r\n\r\n  .solution-container .cramer-badges { gap: 6px; }\r\n  .solution-container .cramer-badge { font-size: .72rem; padding: 3px 8px; }\r\n\r\n  .solution-container .cramer-details > summary {\r\n    padding: 7px 10px;\r\n    border-radius: 8px;\r\n  }\r\n}\r\n\r\n\/* ===================== \u0414\u0420\u0423\u041a ===================== *\/\r\n@media print {\r\n  .solution-container,\r\n  .solution-container .cramer-step {\r\n    box-shadow: none;\r\n    background: #fff;\r\n  }\r\n  .solution-container .cramer-step::before,\r\n  .solution-container .cramer-step::after { display: none; }\r\n}\r\n\r\n\/* ===== \u0414\u0415\u041b\u042c\u0422\u0410-\u0421\u0422\u0418\u041b\u0406 (\u0434\u043e\u0434\u0430\u044e\u0442\u044c\u0441\u044f \u0434\u043e \u0432\u0430\u0448\u043e\u0433\u043e CSS) ===== *\/\r\n.matrix-controls{\r\n  display:flex;\r\n  gap:12px;\r\n  flex-wrap:wrap;\r\n  align-items:flex-end;\r\n}\r\n.matrix-controls__item{ display:flex; flex-direction:column; gap:8px; }\r\n.matrix-controls__item--actions{ margin-left:auto; }\r\n.matrix-actions{ display:flex; gap:10px; flex-wrap:wrap; }\r\n\r\n\/* \u0420\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u0443\u0454\u0442\u044c\u0441\u044f \u043f\u0440\u0438\u0432\u2019\u044f\u0437\u0430\u0442\u0438 \u0434\u043e \u043a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440\u0430 \u043a\u0430\u043b\u044c\u043a\u0443\u043b\u044f\u0442\u043e\u0440\u0430, \u0449\u043e\u0431 \u0442\u043e\u0447\u043d\u043e \u043f\u0435\u0440\u0435\u0431\u0438\u0442\u0438 \u0442\u0435\u043c\u0443 *\/\r\n.calculator-container .btn-secondary{\r\n  height:44px;\r\n  padding:0 14px;\r\n  border-radius:12px;\r\n  border:1px solid var(--ui-border);\r\n  background: var(--ui-panel);\r\n  color: var(--ui-text);\r\n  font-weight:800;\r\n  cursor:pointer;\r\n\r\n  appearance:none;\r\n  -webkit-appearance:none;\r\n  -webkit-tap-highlight-color: transparent;\r\n\r\n  outline: none; \/* \u0442\u0435\u043c\u0430 \u0447\u0430\u0441\u0442\u043e \u0434\u043e\u0434\u0430\u0454 outline + \u0444\u043e\u043d *\/\r\n  transition: box-shadow .15s ease, border-color .15s ease, transform .05s ease, filter .15s ease, background-color .2s ease, color .2s ease;\r\n}\r\n\r\n\/* Hover \/ focus-visible \u2014 \u043a\u0440\u0430\u0441\u0438\u0432\u0438\u0439 \u201c\u0430\u043a\u0446\u0435\u043d\u0442\u043d\u0438\u0439\u201d \u0441\u0442\u0430\u043d *\/\r\n.calculator-container .btn-secondary:hover,\r\n.calculator-container .btn-secondary:focus-visible{\r\n  border-color: var(--ui-accent);\r\n  background: var(--ui-accent);\r\n  color:#fff;\r\n  filter: brightness(1.02);\r\n  box-shadow: 0 10px 24px rgba(11,99,139,.12);\r\n}\r\n\r\n\/* \u041e\u0441\u044c \u043a\u043b\u044e\u0447: \u043f\u0456\u0441\u043b\u044f \u043a\u043b\u0456\u043a\u0443 \u043a\u043d\u043e\u043f\u043a\u0430 \u0443 \u0444\u043e\u043a\u0443\u0441\u0456 \u2014 \u041d\u0415 \u0434\u043e\u0437\u0432\u043e\u043b\u044f\u0454\u043c\u043e \u0442\u0435\u043c\u043d\u043e-\u0441\u0456\u0440\u0438\u0439 \u0444\u043e\u043d *\/\r\n.calculator-container .btn-secondary:focus{\r\n  background: var(--ui-panel) !important;\r\n  color: var(--ui-text) !important;\r\n  border-color: var(--ui-border) !important;\r\n  box-shadow: none !important;\r\n}\r\n\r\n\/* \u041d\u0430\u0442\u0438\u0441\u043a\u0430\u043d\u043d\u044f *\/\r\n.calculator-container .btn-secondary:active{\r\n  background: var(--ui-accent) !important; \/* \u0449\u043e\u0431 \u043d\u0435 \u201c\u0441\u0456\u0440\u0456\u043b\u043e\u201d *\/\r\n  color:#fff !important;\r\n  filter: brightness(0.95); \r\n  transform: translateY(1px);\r\n}\r\n\r\n\/* \u0412\u0438\u043c\u043a\u043d\u0435\u043d\u0438\u0439 \u0441\u0442\u0430\u043d *\/\r\n.calculator-container .btn-secondary:disabled{\r\n  opacity:.55;\r\n  cursor:not-allowed;\r\n  box-shadow:none !important;\r\n  filter:none;\r\n  transform:none;\r\n}\r\n\r\n\r\n\r\n\/* \u041d\u0430\u043b\u0430\u0448\u0442\u0443\u0432\u0430\u043d\u043d\u044f \u0440\u0430\u043d\u0434\u043e\u043c\u0443 *\/\r\n.random-settings{\r\n  margin-top: 12px;\r\n  border: 1px solid var(--ui-border);\r\n  border-radius: 12px;\r\n  background: var(--ui-panel);\r\n  padding: 10px 12px;\r\n}\r\n.random-settings > summary{\r\n  cursor:pointer;\r\n  font-weight:800;\r\n  color: var(--ui-text);\r\n  list-style:none;\r\n}\r\n.random-settings > summary::-webkit-details-marker{ display:none; }\r\n.random-settings > summary::before{\r\n  content:\"\u25b8\";\r\n  display:inline-block;\r\n  margin-right:8px;\r\n  transition: transform .2s ease;\r\n}\r\n.random-settings[open] > summary::before{ transform: rotate(90deg); }\r\n\r\n.random-settings__grid{\r\n  margin-top: 12px;\r\n  display:grid;\r\n  grid-template-columns: repeat(3, minmax(160px, 1fr));\r\n  gap: 12px;\r\n}\r\n.random-settings__item{ display:flex; flex-direction:column; gap:6px; }\r\n\r\n.random-settings__item input[type=\"text\"],\r\n.random-settings__item select{\r\n  height:44px;\r\n  border-radius:12px;\r\n  border:1px solid var(--ui-border);\r\n  background: #fff;\r\n  color: var(--ui-text);\r\n  padding: 0 12px;\r\n  font-weight:700;\r\n  outline:none;\r\n}\r\n@media (prefers-color-scheme: dark){\r\n  .random-settings__item input[type=\"text\"],\r\n  .random-settings__item select{ background: #0f1a22; }\r\n}\r\n@media (max-width:768px){\r\n  .matrix-controls__item--actions{ margin-left:0; width:100%; }\r\n  .matrix-actions{ width:100%; }\r\n  .btn-secondary{ width:100%; }\r\n  .random-settings__grid{ grid-template-columns: 1fr; }\r\n}\r\n\r\n\/* sr-only *\/\r\n.sr-only{\r\n  position:absolute !important;\r\n  width:1px; height:1px;\r\n  padding:0; margin:-1px;\r\n  overflow:hidden; clip:rect(0,0,0,0);\r\n  border:0;\r\n}\r\n<\/style>\r\n\r\n<script>\r\n\/* =========================\r\n   Utilities and state\r\n========================= *\/\r\n\r\nlet activeController = null;\r\n\r\nconst AJAX_URL = (typeof window !== 'undefined' && window.ajaxurl)\r\n  ? window.ajaxurl\r\n  : '\/en\/wp-admin\/admin-ajax.php';\r\n\r\n\/** Show\/hide loader *\/\r\nfunction setLoading(isLoading){\r\n  const loading = document.getElementById('loading');\r\n  if (loading) loading.style.display = isLoading ? 'block' : 'none';\r\n}\r\n\r\n\/** Enable\/disable button *\/\r\nfunction setGenerateDisabled(disabled){\r\n  const btn = document.getElementById('generate-button');\r\n  if (btn) btn.disabled = !!disabled;\r\n}\r\n\r\n\/** Display an error *\/\r\nfunction showError(message){\r\n  const el = document.getElementById('error-block');\r\n  if (!el) return;\r\n  el.textContent = message || 'Something went wrong.';\r\n  el.classList.add('show');\r\n}\r\n\r\n\/** Hide error *\/\r\nfunction clearError(){\r\n  const el = document.getElementById('error-block');\r\n  if (!el) return;\r\n  el.textContent = '';\r\n  el.classList.remove('show');\r\n}\r\n\r\n\/** Heading shown before the steps *\/\r\nfunction buildHeadingHTML(){\r\n  return `\r\n    <h2 class=\"cramer-heading\" role=\"heading\" aria-level=\"2\">\r\n      <span class=\"cramer-heading__title\">Inverse of a Matrix \u2014 Gauss\u2013Jordan Method<\/span>\r\n      <span class=\"cramer-heading__meta\">A\u207b\u00b9 for A \u2208 \u211d\u207f\u02e3\u207f \u2022 Key idea: transform [A|I] \u2192 [I|A\u207b\u00b9] using elementary row operations<\/span>\r\n    <\/h2>\r\n  `;\r\n}\r\n\r\n\/* =========================\r\n   Number normalization\/parsing\r\n========================= *\/\r\n\r\nfunction normalizeNumberInput(value){\r\n  let s = String(value ?? '').trim();\r\n  if (!s) return '';\r\n\r\n  s = s.replace(\/\\s+\/g, '').replace(',', '.');\r\n  s = s.replace(\/[^0-9\\-.]\/g, '');\r\n  s = s.replace(\/(?!^)-\/g, '');\r\n\r\n  const parts = s.split('.');\r\n  if (parts.length > 2){\r\n    s = parts[0] + '.' + parts.slice(1).join('');\r\n  }\r\n\r\n  return s;\r\n}\r\n\r\nfunction parseNumberSafe(val){\r\n  const v = normalizeNumberInput(val);\r\n  if (v === '') return 0;\r\n  if (v === '-' || v === '.' || v === '-.') return null;\r\n\r\n  const n = Number(v);\r\n  return Number.isFinite(n) ? n : null;\r\n}\r\n\r\n\/* =========================\r\n   MathJax v2 (targeted typeset)\r\n========================= *\/\r\n\r\nfunction renderMathJax(container, tries = 12){\r\n  const el = container || document.getElementById('fcontainer');\r\n  if (!el) return;\r\n\r\n  if (window.MathJax && MathJax.Hub && MathJax.Hub.Queue){\r\n    MathJax.Hub.Queue([\"Typeset\", MathJax.Hub, el]);\r\n    return;\r\n  }\r\n  if (tries > 0){\r\n    setTimeout(() => renderMathJax(el, tries - 1), 120);\r\n  }\r\n}\r\n\r\n\/* =========================\r\n   Build\/change input grid\r\n========================= *\/\r\n\r\nfunction clearResult(){\r\n  const resultC = document.getElementById('fcontainer');\r\n  if (resultC){\r\n    resultC.innerHTML = '';\r\n    resultC.style.display = 'none';\r\n  }\r\n}\r\n\r\nfunction removeInputErrorStyles(){\r\n  const table = document.getElementById('matrixTable');\r\n  if (!table) return;\r\n  table.querySelectorAll('input.input-error').forEach(inp => inp.classList.remove('input-error'));\r\n}\r\n\r\nfunction changeMatrixSize(){\r\n  const sizeSel = document.getElementById('matrixSize');\r\n  const size = Number(sizeSel ? sizeSel.value : 3) || 3;\r\n\r\n  clearResult();\r\n  clearError();\r\n  removeInputErrorStyles();\r\n\r\n  const table = document.getElementById('matrixTable');\r\n  if (!table) return;\r\n\r\n  while (table.rows.length > 0) table.deleteRow(0);\r\n\r\n  for (let i=0; i<size; i++){\r\n    const row = table.insertRow(-1);\r\n\r\n    for (let j=0; j<size; j++){\r\n      const cell = row.insertCell(-1);\r\n      const input = document.createElement('input');\r\n\r\n      input.type = 'text';\r\n      input.name = `A[${i}][${j}]`;\r\n      input.placeholder = '0';\r\n      input.inputMode = 'decimal';\r\n      input.autocomplete = 'off';\r\n      input.spellcheck = false;\r\n\r\n      input.addEventListener('input', () => {\r\n        const fixed = normalizeNumberInput(input.value);\r\n        if (input.value !== fixed) input.value = fixed;\r\n        if (input.classList.contains('input-error')){\r\n          input.classList.remove('input-error');\r\n        }\r\n      });\r\n\r\n      input.addEventListener('keydown', (e) => {\r\n        const allowed = [\r\n          'Backspace','Delete','Tab','Enter','Escape',\r\n          'ArrowLeft','ArrowRight','Home','End',\r\n          '-', '.', ',',\r\n        ];\r\n\r\n        if (\r\n          allowed.includes(e.key) ||\r\n          (e.key.length === 1 && \/[0-9]\/.test(e.key)) ||\r\n          e.ctrlKey || e.metaKey\r\n        ) return;\r\n\r\n        e.preventDefault();\r\n      });\r\n\r\n      cell.appendChild(input);\r\n    }\r\n  }\r\n}\r\n\r\n\/* =========================\r\n   Collect matrix from DOM + validation\r\n========================= *\/\r\n\r\nfunction collectMatrix(){\r\n  const table = document.getElementById('matrixTable');\r\n  if (!table) return { matrix: [], invalidCount: 0 };\r\n\r\n  let invalidCount = 0;\r\n  const matrix = [];\r\n\r\n  for (let i=0; i<table.rows.length; i++){\r\n    const row = table.rows[i];\r\n    const rowVals = [];\r\n\r\n    for (let j=0; j<row.cells.length; j++){\r\n      const input = row.cells[j].querySelector('input');\r\n      const raw = input ? input.value : '';\r\n      const parsed = parseNumberSafe(raw);\r\n\r\n      if (parsed === null){\r\n        invalidCount++;\r\n        if (input) input.classList.add('input-error');\r\n        rowVals.push(0);\r\n      } else {\r\n        rowVals.push(parsed);\r\n      }\r\n    }\r\n\r\n    matrix.push(rowVals);\r\n  }\r\n\r\n  return { matrix, invalidCount };\r\n}\r\n\r\n\/* =========================\r\n   Render solution\r\n========================= *\/\r\n\r\nfunction renderSolutionIntoContainer(resultC, payload){\r\n  const heading = buildHeadingHTML();\r\n\r\n  let html = heading + '<div class=\"cramer-solution\">';\r\n\r\n  if (Array.isArray(payload)){\r\n    const texts = payload[2] || [];\r\n    const forms = payload[1] || [];\r\n    const n = Math.max(texts.length, forms.length);\r\n\r\n    for (let i=0; i<n; i++){\r\n      html += '<section class=\"cramer-step\">';\r\n      if (texts[i]) html += texts[i];\r\n      if (forms[i]) html += '<div class=\"formula\">' + forms[i] + '<\/div>';\r\n      html += '<\/section>';\r\n    }\r\n  } else {\r\n    html += '<section class=\"cramer-step\"><div class=\"formula\">\\\\[' + payload + '\\\\]<\/div><\/section>';\r\n  }\r\n\r\n  html += '<\/div>';\r\n  resultC.innerHTML = html;\r\n}\r\n\r\n\/* =========================\r\n   Send to backend and show result\r\n========================= *\/\r\n\r\nfunction sendMatrixToServer(matrix){\r\n  const resultC = document.getElementById('fcontainer');\r\n\r\n  clearResult();\r\n  clearError();\r\n\r\n  if (activeController){\r\n    try { activeController.abort(); } catch(_) {}\r\n  }\r\n  activeController = new AbortController();\r\n\r\n  setLoading(true);\r\n  setGenerateDisabled(true);\r\n\r\n  const fd = new FormData();\r\n  \/\/ \u2705 IMPORTANT: action for your PHP endpoint\r\n  fd.append('action', 'calculate_inverse_matrix_gauss_jordan');\r\n  fd.append('matrix', JSON.stringify(matrix));\r\n\r\n  fetch(AJAX_URL, {\r\n    method: 'POST',\r\n    body: fd,\r\n    signal: activeController.signal\r\n  })\r\n    .then(res => {\r\n      if (!res.ok) throw new Error('Network response was not ok');\r\n      return res.json();\r\n    })\r\n    .then(data => {\r\n      setLoading(false);\r\n      setGenerateDisabled(false);\r\n\r\n      if (!resultC) return;\r\n\r\n      const payload = data.solution; \/\/ expected format [0],[1],[2]\r\n\r\n      if (data.success && payload){\r\n        renderSolutionIntoContainer(resultC, payload);\r\n        renderMathJax(resultC);\r\n\r\n        resultC.style.display = 'block';\r\n        resultC.scrollIntoView({ behavior: 'smooth', block: 'start' });\r\n      } else {\r\n        showError(data.error || 'The server couldn\u2019t process your request.');\r\n      }\r\n    })\r\n    .catch(err => {\r\n      if (err && err.name === 'AbortError') return;\r\n\r\n      setLoading(false);\r\n      setGenerateDisabled(false);\r\n      showError(err.message || 'Network error. Please try again.');\r\n    });\r\n}\r\n\r\n\/* =========================\r\n   Public handler\r\n========================= *\/\r\n\r\nfunction calculateInverseMatrix(){\r\n  clearError();\r\n  removeInputErrorStyles();\r\n\r\n  const { matrix, invalidCount } = collectMatrix();\r\n\r\n  if (!matrix.length){\r\n    showError('Please enter the matrix values.');\r\n    return;\r\n  }\r\n\r\n  if (invalidCount > 0){\r\n    showError('Some entries are invalid. Please fix the highlighted fields.');\r\n    return;\r\n  }\r\n\r\n  sendMatrixToServer(matrix);\r\n}\r\n\r\n\/* =========================\r\n   Clear \/ Fill randomly\r\n========================= *\/\r\nfunction clearMatrix(){\r\n  const table = document.getElementById('matrixTable');\r\n  if (!table) return;\r\n\r\n  table.querySelectorAll('input[type=\"text\"]').forEach(inp => {\r\n    inp.value = '';\r\n    inp.classList.remove('input-error');\r\n  });\r\n\r\n  clearError();\r\n  clearResult();\r\n}\r\n\r\nfunction getRandomSettings(){\r\n  const minEl = document.getElementById('randMin');\r\n  const maxEl = document.getElementById('randMax');\r\n  const decEl = document.getElementById('randDecimals');\r\n\r\n  const minV = parseNumberSafe(minEl ? minEl.value : '-5');\r\n  const maxV = parseNumberSafe(maxEl ? maxEl.value : '5');\r\n  const decimals = Number(decEl ? decEl.value : 0) || 0;\r\n\r\n  if (minV === null || maxV === null){\r\n    return { ok:false, error:'Your random fill settings look invalid (min\/max).' };\r\n  }\r\n  if (maxV < minV){\r\n    return { ok:false, error:'Maximum must be greater than or equal to the minimum.' };\r\n  }\r\n  if (decimals < 0 || decimals > 6){\r\n    return { ok:false, error:'Decimal places must be between 0 and 6.' };\r\n  }\r\n\r\n  return { ok:true, min:minV, max:maxV, decimals };\r\n}\r\n\r\nfunction randFloat(min, max){\r\n  return Math.random() * (max - min) + min;\r\n}\r\n\r\nfunction fillRandom(){\r\n  const settings = getRandomSettings();\r\n  if (!settings.ok){\r\n    showError(settings.error);\r\n    return;\r\n  }\r\n\r\n  const table = document.getElementById('matrixTable');\r\n  if (!table) return;\r\n\r\n  const { min, max, decimals } = settings;\r\n\r\n  table.querySelectorAll('input[type=\"text\"]').forEach(inp => {\r\n    const v = randFloat(min, max);\r\n    const out = (decimals === 0)\r\n      ? String(Math.round(v))\r\n      : String(Number(v.toFixed(decimals)));\r\n\r\n    inp.value = normalizeNumberInput(out);\r\n    inp.classList.remove('input-error');\r\n  });\r\n\r\n  clearError();\r\n  clearResult();\r\n}\r\n\r\n\/* =========================\r\n   Initialization\r\n========================= *\/\r\n\r\ndocument.addEventListener('DOMContentLoaded', () => {\r\n  changeMatrixSize();\r\n\r\n  const sel = document.getElementById('matrixSize');\r\n  if (sel) sel.addEventListener('change', changeMatrixSize);\r\n\r\n  const table = document.getElementById('matrixTable');\r\n  if (table){\r\n    table.addEventListener('keydown', (e) => {\r\n      if (e.key === 'Enter'){\r\n        e.preventDefault();\r\n        calculateInverseMatrix();\r\n      }\r\n    });\r\n  }\r\n\r\n  const btn = document.getElementById('generate-button');\r\n  if (btn) btn.addEventListener('click', calculateInverseMatrix);\r\n  \r\n  const clearBtn = document.getElementById('clearMatrixBtn');\r\n  if (clearBtn) clearBtn.addEventListener('click', clearMatrix);\r\n\r\n  const randBtn = document.getElementById('fillRandomBtn');\r\n  if (randBtn) randBtn.addEventListener('click', fillRandom);\r\n\r\n  \/\/ Light normalization for min\/max inputs\r\n  const minEl = document.getElementById('randMin');\r\n  const maxEl = document.getElementById('randMax');\r\n  [minEl, maxEl].forEach(el => {\r\n    if (!el) return;\r\n    el.addEventListener('input', () => {\r\n      const fixed = normalizeNumberInput(el.value);\r\n      if (el.value !== fixed) el.value = fixed;\r\n    });\r\n  });\r\n});\r\n<\/script>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-11dcb5d elementor-widget elementor-widget-html\" data-id=\"11dcb5d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"h2-title2\">Inverse of a Matrix Calculator: How Does It Work?<\/h2>\n<img decoding=\"async\" class=\"aligncenter wp-image-10020256 size-full\" src=\"https:\/\/www.mathros.net.ua\/en\/wp-content\/uploads\/2026\/01\/inverse-of-a-matrix-using-gauss-jordan-method-calculator1.jpg\" alt=\"Inverse of a matrix calculator\" width=\"150\" height=\"150\" \/>\n<p class=\"calculator-p\">Inverse of a matrix calculator is a tool where you choose the matrix size (2\u00d72, 3\u00d73, 4\u00d74, and so on), fill the grid with your numbers, and click <em>\u201cFind the inverse of a matrix\u201d<\/em>. Convenient, right? And the best part is that you don\u2019t have to track dozens of row operations yourself\u2014the calculator takes care of them for you.<\/p>\n<p class=\"calculator-p\">Next, the tool uses the <a title=\"Inverse of a matrix using the Gauss\u2013Jordan method\" href=\"https:\/\/www.mathros.net.ua\/en\/inverse-of-a-matrix-using-gauss-jordan-method.html\">Gauss\u2013Jordan method<\/a>. It augments your matrix with an identity matrix of the same size and then transforms the left side step by step into the identity matrix. How does it do that? By applying elementary row operations: swapping rows, multiplying a row by a number, and adding to one row another row multiplied by a coefficient. In the end, once the left side becomes the identity matrix, the right side becomes the <a title=\"Invertible matrix\" href=\"https:\/\/en.wikipedia.org\/wiki\/Invertible_matrix\" target=\"_blank\" rel=\"nofollow noopener\">inverse of a matrix<\/a>.<\/p>\n<p class=\"calculator-p\">And how can you tell when an inverse doesn\u2019t exist? If the matrix is singular (its <a title=\"What is determinant of a matrix\" href=\"https:\/\/www.mathros.net.ua\/en\/determinant-of-a-matrix.html\">determinant<\/a> is zero), there is no inverse\u2014so the calculator will show a message in the error block. If everything is fine, the result and explanation will appear in the solution container, and you\u2019ll see a loading indicator while the calculation runs. Then you can compare the answer with your own work and use it in your problem\u2014exactly what you need.<\/p>\n<style>\n    \/* ===== Intro block (title + image + paragraphs) ===== *\/\n\n\/* Title *\/\n.h2-title2 {\n  \/* typography *\/\n  font-family: system-ui, -apple-system, \"Segoe UI\", Roboto, \"Helvetica Neue\", Arial, \"Noto Sans\", \"Liberation Sans\", sans-serif;\n  font-weight: 800;\n  font-size: clamp(1.25rem, 1.05rem + 1.4vw, 1.9rem); \/* ~20\u201330px *\/\n  line-height: 1.25;\n  letter-spacing: .01em;\n\n  \/* layout *\/\n  text-align: center;\n  max-width: 800px;\n  margin: 18px auto 12px;\n  padding: 0;\n\n  \/* color (better than plain gray) *\/\n  color: #334155; \/* slate-700 *\/\n  text-wrap: balance;\n}\n\n\/* Paragraphs *\/\n.calculator-p {\n  font-family: system-ui, -apple-system, \"Segoe UI\", Roboto, \"Helvetica Neue\", Arial, \"Noto Sans\", \"Liberation Sans\", sans-serif;\n  font-weight: 500;\n  font-size: clamp(0.95rem, 0.9rem + 0.3vw, 1rem); \/* ~15\u201316px *\/\n  line-height: 1.65;\n  color: #475569;   \/* slate-600 *\/\n  max-width: 800px;\n  margin: 10px auto;\n  padding: 0 6px;   \/* tiny breathing room on small screens *\/\n  text-align: center;\n  text-wrap: pretty;\n}\n\n\/* Links inside paragraphs *\/\n.calculator-p a {\n  color: #0b638b;\n  text-decoration: underline;\n  text-underline-offset: 3px;\n  text-decoration-thickness: 1.5px;\n  transition: color .15s ease, text-decoration-color .15s ease;\n}\n.calculator-p a:hover {\n  color: #084e6c;\n  text-decoration-color: currentColor;\n}\n.calculator-p a:focus-visible {\n  outline: none;\n  box-shadow: 0 0 0 3px rgba(11, 99, 139, .25);\n  border-radius: 6px;\n}\n\n\/* Centered image *\/\n.aligncenter {\n  display: block;\n  margin: 16px auto;\n  max-width: min(100%, 220px); \/* cap the size to keep the layout tidy *\/\n  height: auto;\n}\n\n\/* Dark mode *\/\n@media (prefers-color-scheme: dark) {\n  .h2-title2 { color: #e2e8f0; }      \/* slate-200 *\/\n  .calculator-p { color: #b6c3cf; }   \/* soft slate for paragraphs *\/\n  .calculator-p a { color: #5ac2f2; }\n  .calculator-p a:hover { color: #82d6fa; }\n}\n\n\/* Tablet tweaks *\/\n@media (max-width: 768px) {\n  .h2-title2 { margin: 16px auto 10px; }\n  .calculator-p { margin: 8px auto; }\n}\n\n\/* Small phones *\/\n@media (max-width: 480px) {\n  .aligncenter { max-width: min(100%, 180px); }\n}\n<\/style>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Checking Your Solution or Starting from Scratch? This Online Calculator Helps You Find the Inverse of a Matrix Accurately\u2014no Mistakes<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-centered.php","meta":{"footnotes":""},"class_list":["post-2322","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/pages\/2322","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/comments?post=2322"}],"version-history":[{"count":51,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/pages\/2322\/revisions"}],"predecessor-version":[{"id":2498,"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/pages\/2322\/revisions\/2498"}],"wp:attachment":[{"href":"https:\/\/www.mathros.net.ua\/en\/wp-json\/wp\/v2\/media?parent=2322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}