{"id":725,"date":"2024-10-28T15:33:58","date_gmt":"2024-10-28T15:33:58","guid":{"rendered":"https:\/\/www.mathros.net.ua\/en\/?page_id=725"},"modified":"2024-10-28T17:16:48","modified_gmt":"2024-10-28T17:16:48","slug":"jacobi-method-calculator","status":"publish","type":"page","link":"https:\/\/www.mathros.net.ua\/en\/jacobi-method-calculator","title":{"rendered":"Jacobi Method Calculator Step by Step"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"725\" class=\"elementor elementor-725\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fb795b8 e-flex e-con-boxed e-con e-parent\" data-id=\"fb795b8\" 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-a16ead6 elementor-widget elementor-widget-html\" data-id=\"a16ead6\" 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\">Are Systems of Linear Equations Giving You a Hard Time? Try Our Tool for Fast, Simple, and Stress-free Solutions Every Time!<\/h2>\n<style>\n    .h2-title {\n        text-align: center; \/* \u0412\u0438\u0440\u0456\u0432\u043d\u044e\u0432\u0430\u043d\u043d\u044f \u043f\u043e \u0446\u0435\u043d\u0442\u0440\u0443 *\/\n        color: gray; \/* \u0417\u0431\u0435\u0440\u0435\u0436\u0435\u043d\u043d\u044f \u0441\u0456\u0440\u043e\u0433\u043e \u043a\u043e\u043b\u044c\u043e\u0440\u0443 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        font-size: 24px; \/* \u0422\u0440\u043e\u0445\u0438 \u0431\u0456\u043b\u044c\u0448\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        font-weight: 600; \/* \u041d\u0430\u043f\u0456\u0432\u0436\u0438\u0440\u043d\u0438\u0439 \u0448\u0440\u0438\u0444\u0442 \u0434\u043b\u044f \u0430\u043a\u0446\u0435\u043d\u0442\u0443 *\/\n        line-height: 1.4; \/* \u041a\u043e\u043c\u0444\u043e\u0440\u0442\u043d\u0438\u0439 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id=\"matrixSize\" name=\"matrixSize\" onchange=\"changeMatrixSize()\">\n          <option value=\"2\">2x2<\/option> \n          <option value=\"3\" selected>3x3<\/option>  \n          <option value=\"4\">4x4<\/option>\n          <option value=\"5\">5x5<\/option>  \n          <option value=\"6\">6x6<\/option>  \n          <option value=\"7\">7x7<\/option>  \n          <option value=\"8\">8x8<\/option>  \n        <\/select>\n    <label for=\"matrixTable\">Augmented Matrix<\/label>    \n <table id=\"matrixTable\" name=\"matrixTable\">\n    <tr>\n        <td>\n            <input type=\"text\" name=\"A[0][0]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"A[0][1]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"A[0][2]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"A[0][3]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n    <\/tr>\n    <tr>\n        <td>\n            <input type=\"text\" name=\"A[1][0]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"A[1][1]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"A[1][2]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"A[1][3]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n    <\/tr> \n    <tr>\n        <td>\n            <input type=\"text\" name=\"A[2][0]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"A[2][1]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"A[2][2]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"A[2][3]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n    <\/tr>\n <\/table>\n    <label for=\"num_partitions\">Calculation Precision (\u03b5)<\/label>\n    <select id=\"epsilon\" name=\"epsilon\">\n        <option selected value=\"0.1\">0.1<\/option>\n        <option value=\"0.01\">0.01<\/option>\n        <option value=\"0.001\">0.001<\/option>\n    <\/select><br\/>\n    <label for=\"vectorTable\" id=\"initial_approximation\">Initial Approximation<\/label>\n <table id=\"vectorTable\" name=\"vectorTable\">\n    <tr>\n        <td>\n            <input type=\"text\" name=\"X0[0]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"X0[1]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n        <td>\n            <input type=\"text\" name=\"X0[2]\" value=\"\" maxlength=\"7\" \/>\n        <\/td>\n    <\/tr>\n <\/table>\n <input type=\"button\" id=\"generate-button\" name=\"solution\" value=\"Solve\" onclick=\"solveSystemOfEquations()\" \/>\n    <div id=\"info-block\" class=\"info-message\">\n        To ensure solvability, make sure there is <strong>diagonal dominance<\/strong> or work with a \n        <strong>positive definite symmetric matrix<\/strong> of coefficients.\n    <\/div>\n<\/div>\n<div id=\"fcontainer\" class=\"solution-container\" style=\"display: none;\"><\/div>\n<div id=\"error-block\" class=\"error-message\"><\/div>\n<div id=\"loading\" class=\"loader\" style=\"display: none;\"><\/div>\n\n<style>\n    body {\n        font-family: 'Arial', sans-serif;\n        margin: 0;\n        padding: 0;\n        background-color: #f4f4f4;\n    }\n    \n    .info-message {\n        background-color: #eaf6ff; \/* \u0421\u0432\u0456\u0442\u043b\u043e-\u0431\u043b\u0430\u043a\u0438\u0442\u043d\u0438\u0439 \u0444\u043e\u043d \u0434\u043b\u044f \u0432\u0438\u0434\u0456\u043b\u0435\u043d\u043d\u044f *\/\n        color: #0b638b; \/* \u0422\u0435\u043c\u043d\u043e-\u0441\u0438\u043d\u0456\u0439 \u0442\u0435\u043a\u0441\u0442 *\/\n        border-left: 4px solid #0b638b; \/* 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*\/\n        margin-top: 15px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u0437\u0432\u0435\u0440\u0445\u0443 *\/\n        margin-bottom: 15px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u0437\u043d\u0438\u0437\u0443 *\/\n        font-family: 'Arial', sans-serif; \/* \u0417\u0440\u0443\u0447\u043d\u0438\u0439 \u0448\u0440\u0438\u0444\u0442 *\/\n        font-size: 16px; \/* \u0420\u043e\u0437\u043c\u0456\u0440 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        color: #333; \/* \u0422\u0435\u043c\u043d\u0438\u0439 \u0442\u0435\u043a\u0441\u0442 \u0434\u043b\u044f \u043a\u043e\u043d\u0442\u0440\u0430\u0441\u0442\u0443 *\/\n        line-height: 1.6; \/* \u0417\u0431\u0456\u043b\u044c\u0448\u0435\u043d\u0438\u0439 \u043c\u0456\u0436\u0440\u044f\u0434\u043a\u043e\u0432\u0438\u0439 \u0456\u043d\u0442\u0435\u0440\u0432\u0430\u043b *\/\n        max-width: 800px; \/* \u041c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u0430 \u0448\u0438\u0440\u0438\u043d\u0430 \u0431\u043b\u043e\u043a\u0443 *\/\n        margin-left: auto; \/* \u0426\u0435\u043d\u0442\u0440\u0443\u0432\u0430\u043d\u043d\u044f \u0431\u043b\u043e\u043a\u0443 *\/\n        margin-right: auto;\n        overflow-x: auto; \/* \u041f\u0440\u043e\u043a\u0440\u0443\u0442\u043a\u0430 \u0434\u043b\u044f \u0434\u043e\u0432\u0433\u0438\u0445 \u0442\u0435\u043a\u0441\u0442\u0456\u0432 \u0430\u0431\u043e \u0444\u043e\u0440\u043c\u0443\u043b *\/\n    }\n\n    \/* \u0410\u0434\u0430\u043f\u0442\u0430\u0446\u0456\u044f \u0434\u043b\u044f \u043c\u043e\u0431\u0456\u043b\u044c\u043d\u0438\u0445 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u0457\u0432 *\/\n    @media (max-width: 768px) {\n        .solution-container {\n            padding: 15px; \/* \u0417\u043c\u0435\u043d\u0448\u0435\u043d\u043d\u044f \u0432\u0456\u0434\u0441\u0442\u0443\u043f\u0456\u0432 \u0434\u043b\u044f \u043f\u043b\u0430\u043d\u0448\u0435\u0442\u0456\u0432 *\/\n        font-size: 14px; \/* \u041c\u0435\u043d\u0448\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        }\n    }\n\n    @media (max-width: 480px) {\n        .solution-container {\n            padding: 10px; \/* \u041c\u0456\u043d\u0456\u043c\u0430\u043b\u044c\u043d\u0456 \u0432\u0456\u0434\u0441\u0442\u0443\u043f\u0438 \u0434\u043b\u044f \u043c\u043e\u0431\u0456\u043b\u044c\u043d\u0438\u0445 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u0457\u0432 *\/\n            font-size: 12px; \/* \u041e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u0438\u0439 \u0440\u043e\u0437\u043c\u0456\u0440 \u0442\u0435\u043a\u0441\u0442\u0443 \u0434\u043b\u044f \u0441\u043c\u0430\u0440\u0442\u0444\u043e\u043d\u0456\u0432 *\/\n        }\n    }\n\n    .solution-container h3 {\n        font-size: 20px; \/* \u0420\u043e\u0437\u043c\u0456\u0440 \u0437\u0430\u0433\u043e\u043b\u043e\u0432\u043a\u0430 *\/\n        color: #333; \/* \u041a\u043e\u043b\u0456\u0440 \u0437\u0430\u0433\u043e\u043b\u043e\u0432\u043a\u0430 *\/\n        margin-bottom: 10px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u043f\u0456\u0434 \u0437\u0430\u0433\u043e\u043b\u043e\u0432\u043a\u043e\u043c *\/\n        text-align: center; \/* \u0426\u0435\u043d\u0442\u0440\u0443\u0432\u0430\u043d\u043d\u044f \u0437\u0430\u0433\u043e\u043b\u043e\u0432\u043a\u0430 *\/\n    }\n\n    .formula {\n        font-family: 'STIX Two Math', serif; \/* \u0428\u0440\u0438\u0444\u0442 \u0434\u043b\u044f \u0444\u043e\u0440\u043c\u0443\u043b *\/\n        background-color: #ffffff; \/* \u0411\u0456\u043b\u0438\u0439 \u0444\u043e\u043d *\/\n        padding: 5px; \/* \u0412\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0456\u0439 \u0432\u0456\u0434\u0441\u0442\u0443\u043f *\/\n        margin-bottom: 5px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u043c\u0456\u0436 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438 *\/\n        overflow-x: auto; \/* \u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430 \u043f\u0440\u043e\u043a\u0440\u0443\u0442\u043a\u0430 \u0434\u043b\u044f \u0432\u0435\u043b\u0438\u043a\u0438\u0445 \u0444\u043e\u0440\u043c\u0443\u043b *\/\n    }\n\n\n    label {\n        display: block;\n        margin-bottom: 8px;\n        font-size: 16px;\n        color: #555;\n        font-weight: 600;\n        text-align: left;\n    }\n    \n    select, input {\n        width: 100%;\n        padding: 10px;\n        margin-bottom: 7px;\n        margin-top: 7px;\n        border: 1px solid #ddd;\n        border-radius: 5px;\n        font-size: 16px;\n    }\n    \n    \n    \/* \u0421\u0442\u0438\u043b\u0456 \u0434\u043b\u044f \u043c\u043e\u0431\u0456\u043b\u044c\u043d\u0438\u0445 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u0457\u0432 *\/\n    @media only screen and (max-width: 768px) {\n        input, select {\n            width: 100%;\n        }\n        #generate-button {\n            width: 100%;\n        }\n        \n    }\n\n    .calculator-container table#matrixTable, .calculator-container table#vectorTable{\n        border-left: 1px solid #ddd;\n        border-right: 1px solid #ddd;\n        margin: 0 auto;\n    }\n\n    .calculator-container table#matrixTable td, .calculator-container table#matrixTable th, .calculator-container table#matrixTable tr, .calculator-container table#vectorTable td, .calculator-container table#vectorTable th, .calculator-container table#vectorTable tr {\n        padding-left: 3px;\n        padding-right: 3px;\n        padding-top: 0;\n        padding-bottom: 0;\n        margin: 0;\n        border-collapse: collapse;\n        border: 0px;\n    }\n    \n    button {\n        width: 100%;\n        padding: 12px;\n        background-color: #0b638b;\n        color: white;\n        border: none;\n        border-radius: 5px;\n        font-size: 18px;\n        cursor: pointer;\n    }\n\n    button:hover {\n        background-color: #065a71;\n    }\n    \n    .loader {\n        margin: 20px auto;\n        border: 8px solid #f3f3f3;\n        border-top: 8px solid #0b638b;\n        border-radius: 50%;\n        width: 50px;\n        height: 50px;\n        animation: spin 1s linear infinite;\n    }\n    \n    @keyframes spin {\n        0% { transform: rotate(0deg); }\n        100% { transform: rotate(360deg); }\n    }\n\n    @media (max-width: 768px) {\n        .calculator-container {\n            padding: 15px;\n        }\n\n        button {\n            font-size: 16px;\n        }\n    }\n    \n    #initial_approximation {\n        \/*font-weight: bold;*\/ \/* \u0420\u043e\u0431\u0438\u0442\u044c \u0442\u0435\u043a\u0441\u0442 \u0436\u0438\u0440\u043d\u0438\u043c *\/\n        color: #c0c0c0; \/* \u0422\u0435\u043c\u043d\u043e-\u0441\u0456\u0440\u0438\u0439 \u043a\u043e\u043b\u0456\u0440 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        cursor: pointer; \/* \u0417\u043c\u0456\u043d\u0430 \u043a\u0443\u0440\u0441\u043e\u0440\u0430 \u043d\u0430 \"\u0440\u0443\u043a\u0443\" \u043f\u0440\u0438 \u043d\u0430\u0432\u0435\u0434\u0435\u043d\u043d\u0456 *\/\n        transition: background-color 0.3s, color 0.3s; \/* \u041f\u043b\u0430\u0432\u043d\u0430 \u0430\u043d\u0456\u043c\u0430\u0446\u0456\u044f \u0437\u043c\u0456\u043d \u0441\u0442\u0438\u043b\u0456\u0432 *\/\n    }\n\n    #initial_approximation:hover {\n        color: #333; \/* \u0422\u0435\u043c\u043d\u0456\u0448\u0438\u0439 \u0442\u0435\u043a\u0441\u0442 \u043f\u0440\u0438 \u043d\u0430\u0432\u0435\u0434\u0435\u043d\u043d\u0456 *\/\n    }\n    \n    .error-message {\n        background-color: #fdecea; \/* \u0421\u0432\u0456\u0442\u043b\u043e-\u0447\u0435\u0440\u0432\u043e\u043d\u0438\u0439 \u0444\u043e\u043d \u0434\u043b\u044f \u043f\u043e\u043c\u0438\u043b\u043e\u043a *\/\n        color: #b71c1c; \/* \u0422\u0435\u043c\u043d\u043e-\u0447\u0435\u0440\u0432\u043e\u043d\u0438\u0439 \u0442\u0435\u043a\u0441\u0442 *\/\n        border-left: 4px solid #b71c1c; \/* \u0421\u0432\u0456\u0442\u043b\u0430 \u0440\u0430\u043c\u043a\u0430 \u0434\u043b\u044f \u0432\u0438\u0434\u0456\u043b\u0435\u043d\u043d\u044f *\/\n        border-radius: 5px; \/* \u0417\u0430\u043e\u043a\u0440\u0443\u0433\u043b\u0435\u043d\u0456 \u043a\u0443\u0442\u0438 *\/\n        padding: 15px; \/* \u0412\u043d\u0443\u0442\u0440\u0456\u0448\u043d\u0456\u0439 \u0432\u0456\u0434\u0441\u0442\u0443\u043f *\/\n        margin-top: 10px; \/* \u0412\u0456\u0434\u0441\u0442\u0443\u043f \u0437\u0432\u0435\u0440\u0445\u0443 *\/\n        font-size: 16px; \/* \u0420\u043e\u0437\u043c\u0456\u0440 \u0442\u0435\u043a\u0441\u0442\u0443 *\/\n        font-family: 'Arial', sans-serif; \/* \u0428\u0440\u0438\u0444\u0442 *\/\n        display: none; \/* \u0421\u043f\u043e\u0447\u0430\u0442\u043a\u0443 \u043f\u0440\u0438\u0445\u043e\u0432\u0430\u043d\u043e *\/\n    }\n\n    .error-message.show {\n        display: block; \/* \u0412\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u043d\u044f \u043f\u0440\u0438 \u043d\u0435\u043e\u0431\u0445\u0456\u0434\u043d\u043e\u0441\u0442\u0456 *\/\n        animation: fadeIn 0.5s ease-in-out; \/* \u041f\u043b\u0430\u0432\u043d\u0430 \u0430\u043d\u0456\u043c\u0430\u0446\u0456\u044f \u043f\u043e\u044f\u0432\u0438 *\/\n    }\n\n    @keyframes fadeIn {\n        0% { opacity: 0; }\n        100% { opacity: 1; }\n    }\n<\/style>\n\n<script>\n\t\/\/ \u0417\u043c\u0456\u043d\u043d\u0430 \u0431\u0443\u043b\u0435\u0432\u043e\u0433\u043e \u0442\u0438\u043f\u0443 \u0434\u043b\u044f \u0432\u0456\u0434\u0441\u0442\u0435\u0436\u0435\u043d\u043d\u044f \u0441\u0442\u0430\u043d\u0443 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 vectorTable\n    var isInitialApproximationVisible = false;\n\n    \/\/ \u0424\u0443\u043d\u043a\u0446\u0456\u044f \u0434\u043b\u044f \u043f\u0440\u0438\u0445\u043e\u0432\u0443\u0432\u0430\u043d\u043d\u044f \u0430\u0431\u043e \u0432\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u043d\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0456\n    function toggleVectorTable() {\n        var vectorTable = document.getElementById('vectorTable');\n        var initialApproximation = document.getElementById('initial_approximation'); \/\/ \u041e\u0442\u0440\u0438\u043c\u0443\u0454\u043c\u043e \u0435\u043b\u0435\u043c\u0435\u043d\u0442 \u0434\u043b\u044f \u0437\u043c\u0456\u043d\u0438 \u043a\u043e\u043b\u044c\u043e\u0440\u0443\n\n        \/\/ \u041f\u0435\u0440\u0435\u0432\u0456\u0440\u043a\u0430, \u0447\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u044f \u043d\u0430\u0440\u0430\u0437\u0456 \u0432\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0430\n        if (vectorTable.style.display === 'none' || vectorTable.style.display === '') {\n            vectorTable.style.display = 'table'; \/\/ \u0412\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0430\u0454\u043c\u043e \u0442\u0430\u0431\u043b\u0438\u0446\u044e\n            isInitialApproximationVisible = true; \/\/ \u0417\u043c\u0456\u043d\u044e\u0454\u043c\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0431\u0443\u043b\u0435\u0432\u043e\u0457 \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u043d\u0430 true\n            initialApproximation.style.color = '#555'; \/\/ \u0417\u043c\u0456\u043d\u044e\u0454\u043c\u043e \u043a\u043e\u043b\u0456\u0440 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\n        } else {\n            vectorTable.style.display = 'none'; \/\/ \u041f\u0440\u0438\u0445\u043e\u0432\u0443\u0454\u043c\u043e \u0442\u0430\u0431\u043b\u0438\u0446\u044e\n            isInitialApproximationVisible = false; \/\/ \u0417\u043c\u0456\u043d\u044e\u0454\u043c\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0431\u0443\u043b\u0435\u0432\u043e\u0457 \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u043d\u0430 false\n            initialApproximation.style.color = ''; \/\/ \u041f\u043e\u0432\u0435\u0440\u0442\u0430\u0454\u043c\u043e \u043a\u043e\u043b\u0456\u0440 \u0437\u0430 \u0437\u0430\u043c\u043e\u0432\u0447\u0443\u0432\u0430\u043d\u043d\u044f\u043c\n        }\n    }\n\n    \/\/ \u0414\u043e\u0434\u0430\u0454\u043c\u043e \u043e\u0431\u0440\u043e\u0431\u043d\u0438\u043a \u043f\u043e\u0434\u0456\u0457 \u0434\u043b\u044f \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430 initial_approximation\n    document.getElementById('initial_approximation').addEventListener('click', toggleVectorTable);\n    \n    \/\/ \u041f\u0440\u0438\u0445\u043e\u0432\u0443\u0454\u043c\u043e \u0442\u0430\u0431\u043b\u0438\u0446\u044e \u043f\u0440\u0438 \u0437\u0430\u0432\u0430\u043d\u0442\u0430\u0436\u0435\u043d\u043d\u0456 \u0441\u0442\u043e\u0440\u0456\u043d\u043a\u0438\n    document.getElementById('vectorTable').style.display = 'none';\n\t\n\t\/\/ JavaScript \u0444\u0443\u043d\u043a\u0446\u0456\u044f \u0434\u043b\u044f \u0437\u043c\u0456\u043d\u0438 \u0440\u043e\u0437\u043c\u0456\u0440\u0443 \u043c\u0430\u0442\u0440\u0438\u0446\u0456\n    function changeMatrixSize() {\n        \/\/ \u041e\u0442\u0440\u0438\u043c\u0430\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043f\u043e\u043b\u044f \u0432\u0438\u0431\u043e\u0440\u0443\n        var size = document.getElementById('matrixSize').value;\n        var resultC = document.getElementById('fcontainer');\n        \n        resultC.innerHTML = '';\n        resultC.style.display = 'none';\n\n        \/\/ \u0417\u043c\u0456\u043d\u0438\u0442\u0438 \u0440\u043e\u0437\u043c\u0456\u0440 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 \u043d\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043f\u043e\u043b\u044f \u0432\u0438\u0431\u043e\u0440\u0443\n        var table = document.getElementById('matrixTable');\n        while (table.rows.length > 0) {\n            table.deleteRow(0);\n        }\n\n        for (var i = 0; i < size; i++) {\n            var row = table.insertRow(i);\n            for (var j = 0; j <= size; j++) {\n                var cell = row.insertCell(j);\n                var input = document.createElement('input');\n                input.type = 'text';\n\t\t\t\tinput.name = 'A[' + i + '][' + j + ']';\n                cell.appendChild(input);\n            }\n        }\n        \n        \/\/ \u0417\u043c\u0456\u043d\u0438\u0442\u0438 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u0441\u0442\u043e\u0432\u043f\u0446\u0456\u0432 \u0443 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 vectorTable\n        var vectorTable = document.getElementById('vectorTable');\n        var vectorRow = vectorTable.rows[0];\n\n        \/\/ \u0412\u0438\u0434\u0430\u043b\u0438\u0442\u0438 \u0432\u0441\u0456 \u0456\u0441\u043d\u0443\u044e\u0447\u0456 \u0441\u0442\u043e\u0432\u043f\u0446\u0456 \u0443 vectorTable\n        while (vectorRow.cells.length > 0) {\n            vectorRow.deleteCell(0);\n        }\n\n        \/\/ \u0414\u043e\u0434\u0430\u0442\u0438 \u043d\u043e\u0432\u0456 \u0441\u0442\u043e\u0432\u043f\u0446\u0456 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u043d\u043e \u0434\u043e \u0440\u043e\u0437\u043c\u0456\u0440\u0443 \u043c\u0430\u0442\u0440\u0438\u0446\u0456\n        for (var i = 0; i < size; i++) {\n            var cell = vectorRow.insertCell(i);\n            var input = document.createElement('input');\n            input.type = 'text';\n            input.name = 'X0[' + i + ']';\n            input.maxLength = 7;\n            cell.appendChild(input);\n        }\n    }\n\n    function solveSystemOfEquations() {\n        var matrixTable = document.getElementById('matrixTable');\n        var epsilon = document.getElementById('epsilon');\n        var vectorTable = document.getElementById('vectorTable');\n\n        \/\/ \u0406\u043d\u0456\u0446\u0456\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u044f \u0434\u0432\u043e\u0432\u0438\u043c\u0456\u0440\u043d\u043e\u0433\u043e \u043c\u0430\u0441\u0438\u0432\u0443 \u0434\u043b\u044f \u0437\u0431\u0435\u0440\u0435\u0436\u0435\u043d\u043d\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u0456\n        var matrix = [];\n        \/\/ \u0406\u043d\u0456\u0446\u0456\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u044f \u043e\u0434\u043d\u043e\u0432\u0438\u043c\u0456\u0440\u043d\u043e\u0433\u043e \u043c\u0430\u0441\u0438\u0432\u0443 \u0434\u043b\u044f \u0437\u0431\u0435\u0440\u0435\u0436\u0435\u043d\u043d\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u044c \u043f\u043e\u0447\u0430\u0442\u043a\u043e\u0432\u043e\u0433\u043e \u043d\u0430\u0431\u043b\u0438\u0436\u0435\u043d\u043d\u044f\n        var vector = [];\n        \/\/ \u0406\u043d\u0456\u0446\u0456\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u044f \u0434\u0432\u043e\u0432\u0438\u043c\u0456\u0440\u043d\u043e\u0433\u043e \u043c\u0430\u0441\u0438\u0432\u0443 \u0434\u043b\u044f \u0437\u0431\u0435\u0440\u0435\u0436\u0435\u043d\u043d\u044f \u0432\u0432\u0435\u0434\u0435\u043d\u0438\u0445 \u043a\u043e\u0440\u0438\u0441\u0442\u0443\u0432\u0430\u0447\u0435\u043c \u0434\u0430\u043d\u0438\u0445\n        var enteredData = []; \n\n        \/\/ \u041f\u0435\u0440\u0435\u0431\u0456\u0440 \u0440\u044f\u0434\u043a\u0456\u0432 \u0442\u0430\u0431\u043b\u0438\u0446\u0456\n        for (var i = 0; i < matrixTable.rows.length; i++) {\n            \/\/ \u041e\u0442\u0440\u0438\u043c\u0430\u043d\u043d\u044f \u043f\u043e\u0441\u0438\u043b\u0430\u043d\u043d\u044f \u043d\u0430 \u043f\u043e\u0442\u043e\u0447\u043d\u0438\u0439 \u0440\u044f\u0434\u043e\u043a\n            var row = matrixTable.rows[i];\n    \n            \/\/ \u0406\u043d\u0456\u0446\u0456\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u044f \u043c\u0430\u0441\u0438\u0432\u0443 \u0434\u043b\u044f \u0437\u0431\u0435\u0440\u0435\u0436\u0435\u043d\u043d\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u044c \u0440\u044f\u0434\u043a\u0430\n            var rowValues = [];\n    \n            \/\/ \u041f\u0435\u0440\u0435\u0431\u0456\u0440 \u043a\u043e\u043c\u0456\u0440\u043e\u043a \u0440\u044f\u0434\u043a\u0430\n            for (var j = 0; j < row.cells.length; j++) {\n                \/\/ \u041e\u0442\u0440\u0438\u043c\u0430\u043d\u043d\u044f \u043f\u043e\u0441\u0438\u043b\u0430\u043d\u043d\u044f \u043d\u0430 \u043f\u043e\u0442\u043e\u0447\u043d\u0443 \u043a\u043e\u043c\u0456\u0440\u043a\u0443\n                var cell = row.cells[j];\n        \n                \/\/ \u041e\u0442\u0440\u0438\u043c\u0430\u043d\u043d\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0432\u0432\u0435\u0434\u0435\u043d\u043d\u044f \u0437 \u043a\u043e\u043c\u0456\u0440\u043a\u0438\n                var inputValue = cell.querySelector('input').value;\n        \n                \/\/ \u0414\u043e\u0434\u0430\u0432\u0430\u043d\u043d\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0434\u043e \u043c\u0430\u0441\u0438\u0432\u0443 \u0440\u044f\u0434\u043a\u0430\n                rowValues.push(parseFloat(inputValue)); \/\/ \u041f\u0435\u0440\u0435\u0442\u0432\u043e\u0440\u0435\u043d\u043d\u044f \u0432 \u0447\u0438\u0441\u043b\u043e, \u0437\u0430 \u0437\u0430\u043c\u043e\u0432\u0447\u0443\u0432\u0430\u043d\u043d\u044f\u043c 0, \u044f\u043a\u0449\u043e \u043d\u0435 \u0432\u0434\u0430\u043b\u043e\u0441\u044f\n            }\n    \n            \/\/ \u0414\u043e\u0434\u0430\u0432\u0430\u043d\u043d\u044f \u043c\u0430\u0441\u0438\u0432\u0443 \u0440\u044f\u0434\u043a\u0430 \u0434\u043e \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0433\u043e \u043c\u0430\u0441\u0438\u0432\u0443 \u043c\u0430\u0442\u0440\u0438\u0446\u0456\n            matrix.push(rowValues);\n        }\n        \n        \/\/ \u041f\u0435\u0440\u0435\u0431\u0456\u0440 \u043a\u043e\u043c\u0456\u0440\u043e\u043a \u0442\u0430\u0431\u043b\u0438\u0446\u0456 \u0437 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c\n        for (var i = 0; i < vectorTable.rows[0].cells.length; i++) {\n            var cell = vectorTable.rows[0].cells[i]; \/\/ \u041f\u043e\u0442\u043e\u0447\u043d\u0430 \u043a\u043e\u043c\u0456\u0440\u043a\u0430\n            var inputValue = 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Imagine having a system of equations that\u2019s tough to solve by hand\u2014our calculator breaks down the process step-by-step, making it clear and manageable. The calculator takes each variable in your system and iteratively adjusts its value based on the surrounding coefficients, steadily bringing you closer to the solution with each step.<\/p>\n<p class=\"calculator-p\">How does it do this? The calculator starts with an initial approximation, which you provide or it generates, and recalculates each variable by isolating it on one side of each equation. It then updates all values simultaneously in each iteration until the solution converges within the desired accuracy you\u2019ve selected. This method ensures that all variables are updated independently, giving an accurate picture of how each step changes the results and moves toward a stable solution.<\/p>\n<p class=\"calculator-p\">Finally, one of the standout features of this Jacobi Method Calculator is that it visually displays each step of the process. 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