{"id":3764,"date":"2025-05-04T01:56:19","date_gmt":"2025-05-04T05:56:19","guid":{"rendered":"https:\/\/calculatorcch.com\/?page_id=3764"},"modified":"2025-05-04T01:56:20","modified_gmt":"2025-05-04T05:56:20","slug":"gauss-jordan-method-calculator","status":"publish","type":"page","link":"https:\/\/calculatorcch.com\/en\/education-and-study-calculators\/gauss-jordan-method-calculator\/","title":{"rendered":"Gauss-Jordan Method Calculator"},"content":{"rendered":"<p>[et_pb_section fb_built=\u201d1\u2033 custom_padding_last_edited=\u201don|desktop\u201d _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d background_color=\u201drgba(214,214,214,0.2)\u201d custom_margin_tablet=\u201d\u201d custom_margin_phone=\u201d\u201d custom_margin_last_edited=\u201don|phone\u201d custom_padding=\u201d0px||0px||false|false\u201d custom_padding_tablet=\u201d22px||22px||true|false\u201d custom_padding_phone=\u201d22px||22px||true|false\u201d bottom_divider_style=\u201dwaves2\u2033 bottom_divider_color=\u201d#0970C4\u2033 bottom_divider_height=\u201d37px\u201d bottom_divider_height_tablet=\u201d37px\u201d bottom_divider_height_phone=\u201d37px\u201d bottom_divider_height_last_edited=\u201don|desktop\u201d background_last_edited=\u201don|desktop\u201d global_colors_info=\u201d{}\u201d][et_pb_row _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d][et_pb_column type=\u201d4_4\u2033 _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d][et_pb_text _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d]<\/p>\n<h1><b>Gauss-Jordan Method Calculator \u2013 Solve Systems of Linear Equations Accurately<\/b><\/h1>\n<p>[\/et_pb_text][et_pb_code _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d custom_margin=\u201d||0px||false|false\u201d custom_margin_tablet=\u201d||0px||false|false\u201d custom_margin_phone=\u201d||0px||false|false\u201d custom_margin_last_edited=\u201don|desktop\u201d custom_padding=\u201d||||false|false\u201d hover_enabled=\u201d0\u2033 global_colors_info=\u201d{}\u201d sticky_enabled=\u201d0\u2033]<\/p>\n<div class=\"roi-calculator-container\"><!-- [et_pb_line_break_holder] -->    <\/p>\n<h2>Gauss-Jordan Method Calculator<\/h2>\n<p><!-- [et_pb_line_break_holder] -->    <\/p>\n<div id=\"ecuacion1\"><!-- [et_pb_line_break_holder] -->        <\/p>\n<h3>Equation 1<\/h3>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"x1_ec1\">Coefficient of x1 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"x1_ec1\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"y1_ec1\">Coefficient of y1 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"y1_ec1\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"z1_ec1\">Coefficient of z1 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"z1_ec1\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"resultado1\">Result 1 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"resultado1\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    <\/p>\n<div id=\"ecuacion2\"><!-- [et_pb_line_break_holder] -->        <\/p>\n<h3>Equation 2<\/h3>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"x2_ec2\">Coefficient of x2 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"x2_ec2\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"y2_ec2\">Coefficient of y2 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"y2_ec2\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"z2_ec2\">Coefficient of z2 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"z2_ec2\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"resultado2\">Result 2 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"resultado2\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    <\/p>\n<div id=\"ecuacion3\"><!-- [et_pb_line_break_holder] -->        <\/p>\n<h3>Equation 3<\/h3>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"x3_ec3\">Coefficient of x3 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"x3_ec3\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"y3_ec3\">Coefficient of y3 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"y3_ec3\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"z3_ec3\">Coefficient of z3 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"z3_ec3\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->        <\/p>\n<div class=\"form-group\"><!-- [et_pb_line_break_holder] -->            <label for=\"resultado3\">Result 3 ($)<\/label><!-- [et_pb_line_break_holder] -->            <input type=\"number\" id=\"resultado3\" step=\"any\"><!-- [et_pb_line_break_holder] -->        <\/div>\n<p><!-- [et_pb_line_break_holder] -->    <\/div>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    <button id=\"resolverSistemaButton\" onclick=\"resolverSistema()\">Solve System<\/button><!-- [et_pb_line_break_holder] -->    <\/p>\n<div class=\"result\" id=\"result\" style=\"margin-top: 20px;\"><\/div>\n<p><!-- [et_pb_line_break_holder] --><\/div>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] --><\/p>\n<style><!-- [et_pb_line_break_holder] -->    \/* INICIO BLOQUE CSS - NO MODIFICAR *\/<!-- [et_pb_line_break_holder] -->    .roi-calculator-container { background: white; padding: 20px; border-radius: 8px; max-width: 500px; margin: 0 auto; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container h2, .roi-calculator-container h3 { font-family: Arial, sans-serif; color: #000000; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container .form-group { margin-bottom: 15px; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container label { display: block; margin-bottom: 5px; font-family: Arial, sans-serif; color: #000000; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container input[type=\"number\"] { width: 100%; padding: 8px; box-sizing: border-box; border: 1px solid #0970C4; border-radius: 4px; font-family: Arial, sans-serif; color: #000000; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container .result { font-family: Arial, sans-serif; color: #000000; padding: 15px; }<!-- [et_pb_line_break_holder] -->    @media (min-width: 981px) { .roi-calculator-container label, .roi-calculator-container input[type=\"number\"], .roi-calculator-container .result { font-size: 20px; } .roi-calculator-container button { font-size: 20px; text-align: center; display: block; margin: 0 auto; } }<!-- [et_pb_line_break_holder] -->    @media (max-width: 980px) and (min-width: 768px) { .roi-calculator-container label, .roi-calculator-container input[type=\"number\"], .roi-calculator-container .result { font-size: 17px; } .roi-calculator-container button { font-size: 20px; text-align: center; display: block; margin: 0 auto; } }<!-- [et_pb_line_break_holder] -->    @media (max-width: 767px) { .roi-calculator-container label, .roi-calculator-container input[type=\"number\"], .roi-calculator-container .result { font-size: 16px; } .roi-calculator-container button { font-size: 20px; text-align: center; display: block; margin: 0 auto; } }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container button { padding: 10px 20px; background-color: #C35D09; color: white; border: none; border-radius: 4px; cursor: pointer; margin-top: 10px; }<!-- [et_pb_line_break_holder] -->    .roi-calculator-container button:hover { background-color: #b35408; }<!-- [et_pb_line_break_holder] -->    \/* FIN BLOQUE CSS - NO MODIFICAR *\/<!-- [et_pb_line_break_holder] --><\/style>\n<p><!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] --><script><!-- [et_pb_line_break_holder] -->    const translations = {<!-- [et_pb_line_break_holder] -->        es: {<!-- [et_pb_line_break_holder] -->            resolverSistemaButton: 'Resolver Sistema',<!-- [et_pb_line_break_holder] -->            x1_ec1Label: 'Coeficiente de x1 ($)',<!-- [et_pb_line_break_holder] -->            y1_ec1Label: 'Coeficiente de y1 ($)',<!-- [et_pb_line_break_holder] -->            z1_ec1Label: 'Coeficiente de z1 ($)',<!-- [et_pb_line_break_holder] -->            resultado1Label: 'Resultado 1 ($)',<!-- [et_pb_line_break_holder] -->            x2_ec2Label: 'Coeficiente de x2 ($)',<!-- [et_pb_line_break_holder] -->            y2_ec2Label: 'Coeficiente de y2 ($)',<!-- [et_pb_line_break_holder] -->            z2_ec2Label: 'Coeficiente de z2 ($)',<!-- [et_pb_line_break_holder] -->            resultado2Label: 'Resultado 2 ($)',<!-- [et_pb_line_break_holder] -->            x3_ec3Label: 'Coeficiente de x3 ($)',<!-- [et_pb_line_break_holder] -->            y3_ec3Label: 'Coeficiente de y3 ($)',<!-- [et_pb_line_break_holder] -->            z3_ec3Label: 'Coeficiente de z3 ($)',<!-- [et_pb_line_break_holder] -->            resultado3Label: 'Resultado 3 ($)',<!-- [et_pb_line_break_holder] -->            solucion: 'La soluci\u00f3n es: x = ',<!-- [et_pb_line_break_holder] -->            ySolucion: ', y = ',<!-- [et_pb_line_break_holder] -->            zSolucion: ', z = ',<!-- [et_pb_line_break_holder] -->            errorDeterminanteCero: 'El sistema no tiene soluci\u00f3n \u00fanica (determinante es cero).',<!-- [et_pb_line_break_holder] -->            errorEntradaInvalida: 'Por favor, introduce coeficientes y resultados v\u00e1lidos.'<!-- [et_pb_line_break_holder] -->        },<!-- [et_pb_line_break_holder] -->        en: {<!-- [et_pb_line_break_holder] -->            resolverSistemaButton: 'Solve System',<!-- [et_pb_line_break_holder] -->            x1_ec1Label: 'Coefficient of x1 ($)',<!-- [et_pb_line_break_holder] -->            y1_ec1Label: 'Coefficient of y1 ($)',<!-- [et_pb_line_break_holder] -->            z1_ec1Label: 'Coefficient of z1 ($)',<!-- [et_pb_line_break_holder] -->            resultado1Label: 'Result 1 ($)',<!-- [et_pb_line_break_holder] -->            x2_ec2Label: 'Coefficient of x2 ($)',<!-- [et_pb_line_break_holder] -->            y2_ec2Label: 'Coefficient of y2 ($)',<!-- [et_pb_line_break_holder] -->            z2_ec2Label: 'Coefficient of z2 ($)',<!-- [et_pb_line_break_holder] -->            resultado2Label: 'Result 2 ($)',<!-- [et_pb_line_break_holder] -->            x3_ec3Label: 'Coefficient of x3 ($)',<!-- [et_pb_line_break_holder] -->            y3_ec3Label: 'Coefficient of y3 ($)',<!-- [et_pb_line_break_holder] -->            z3_ec3Label: 'Coefficient of z3 ($)',<!-- [et_pb_line_break_holder] -->            resultado3Label: 'Result 3 ($)',<!-- [et_pb_line_break_holder] -->            solucion: 'The solution is: x = ',<!-- [et_pb_line_break_holder] -->            ySolucion: ', y = ',<!-- [et_pb_line_break_holder] -->            zSolucion: ', z = ',<!-- [et_pb_line_break_holder] -->            errorDeterminanteCero: 'The system has no unique solution (determinant is zero).',<!-- [et_pb_line_break_holder] -->            errorEntradaInvalida: 'Please enter valid coefficients and results.'<!-- [et_pb_line_break_holder] -->        },<!-- [et_pb_line_break_holder] -->        fr: {<!-- [et_pb_line_break_holder] -->            resolverSistemaButton: 'R\u00e9soudre le Syst\u00e8me',<!-- [et_pb_line_break_holder] -->            x1_ec1Label: 'Coefficient de x1 ($)',<!-- [et_pb_line_break_holder] -->            y1_ec1Label: 'Coefficient de y1 ($)',<!-- [et_pb_line_break_holder] -->            z1_ec1Label: 'Coefficient de z1 ($)',<!-- [et_pb_line_break_holder] -->            resultado1Label: 'R\u00e9sultat 1 ($)',<!-- [et_pb_line_break_holder] -->            x2_ec2Label: 'Coefficient de x2 ($)',<!-- [et_pb_line_break_holder] -->            y2_ec2Label: 'Coefficient de y2 ($)',<!-- [et_pb_line_break_holder] -->            z2_ec2Label: 'Coefficient de z2 ($)',<!-- [et_pb_line_break_holder] -->            resultado2Label: 'R\u00e9sultat 2 ($)',<!-- [et_pb_line_break_holder] -->            x3_ec3Label: 'Coefficient de x3 ($)',<!-- [et_pb_line_break_holder] -->            y3_ec3Label: 'Coefficient de y3 ($)',<!-- [et_pb_line_break_holder] -->            z3_ec3Label: 'Coefficient de z3 ($)',<!-- [et_pb_line_break_holder] -->            resultado3Label: 'R\u00e9sultat 3 ($)',<!-- [et_pb_line_break_holder] -->            solucion: 'La solution est : x = ',<!-- [et_pb_line_break_holder] -->            ySolucion: ', y = ',<!-- [et_pb_line_break_holder] -->            zSolucion: ', z = ',<!-- [et_pb_line_break_holder] -->            errorDeterminanteCero: 'Le syst\u00e8me n\\'a pas de solution unique (d\u00e9terminant est z\u00e9ro).',<!-- [et_pb_line_break_holder] -->            errorEntradaInvalida: 'Veuillez entrer des coefficients et des r\u00e9sultats valides.'<!-- [et_pb_line_break_holder] -->        },<!-- [et_pb_line_break_holder] -->        pt: {<!-- [et_pb_line_break_holder] -->            resolverSistemaButton: 'Resolver Sistema',<!-- [et_pb_line_break_holder] -->            x1_ec1Label: 'Coeficiente de x1 ($)',<!-- [et_pb_line_break_holder] -->            y1_ec1Label: 'Coeficiente de y1 ($)',<!-- [et_pb_line_break_holder] -->            z1_ec1Label: 'Coeficiente de z1 ($)',<!-- [et_pb_line_break_holder] -->            resultado1Label: 'Resultado 1 ($)',<!-- [et_pb_line_break_holder] -->            x2_ec2Label: 'Coeficiente de x2 ($)',<!-- [et_pb_line_break_holder] -->            y2_ec2Label: 'Coeficiente de y2 ($)',<!-- [et_pb_line_break_holder] -->            z2_ec2Label: 'Coeficiente de z2 ($)',<!-- [et_pb_line_break_holder] -->            resultado2Label: 'Resultado 2 ($)',<!-- [et_pb_line_break_holder] -->            x3_ec3Label: 'Coeficiente de x3 ($)',<!-- [et_pb_line_break_holder] -->            y3_ec3Label: 'Coeficiente de y3 ($)',<!-- [et_pb_line_break_holder] -->            z3_ec3Label: 'Coeficiente de z3 ($)',<!-- [et_pb_line_break_holder] -->            resultado3Label: 'Resultado 3 ($)',<!-- [et_pb_line_break_holder] -->            solucion: 'A solu\u00e7\u00e3o \u00e9: x = ',<!-- [et_pb_line_break_holder] -->            ySolucion: ', y = ',<!-- [et_pb_line_break_holder] -->            zSolucion: ', z = ',<!-- [et_pb_line_break_holder] -->            errorDeterminanteCero: 'O sistema n\u00e3o tem solu\u00e7\u00e3o \u00fanica (determinante \u00e9 zero).',<!-- [et_pb_line_break_holder] -->            errorEntradaInvalida: 'Por favor, insira coeficientes e resultados v\u00e1lidos.'<!-- [et_pb_line_break_holder] -->        }<!-- [et_pb_line_break_holder] -->    };<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    document.addEventListener('DOMContentLoaded', (event) => {<!-- [et_pb_line_break_holder] -->        const language = getUserLanguage();<!-- [et_pb_line_break_holder] -->        setLanguage(language);<!-- [et_pb_line_break_holder] -->    });<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    function setLanguage(language) {<!-- [et_pb_line_break_holder] -->        document.getElementById('resolverSistemaButton').innerText = translations[language].resolverSistemaButton;<!-- [et_pb_line_break_holder] -->        document.getElementById('x1_ec1Label').innerText = translations[language].x1_ec1Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('y1_ec1Label').innerText = translations[language].y1_ec1Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('z1_ec1Label').innerText = translations[language].z1_ec1Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('resultado1Label').innerText = translations[language].resultado1Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('x2_ec2Label').innerText = translations[language].x2_ec2Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('y2_ec2Label').innerText = translations[language].y2_ec2Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('z2_ec2Label').innerText = translations[language].z2_ec2Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('resultado2Label').innerText = translations[language].resultado2Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('x3_ec3Label').innerText = translations[language].x3_ec3Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('y3_ec3Label').innerText = translations[language].y3_ec3Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('z3_ec3Label').innerText = translations[language].z3_ec3Label;<!-- [et_pb_line_break_holder] -->        document.getElementById('resultado3Label').innerText = translations[language].resultado3Label;<!-- [et_pb_line_break_holder] -->    }<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    function getUserLanguage() {<!-- [et_pb_line_break_holder] -->        const userLang = navigator.language || navigator.userLanguage;<!-- [et_pb_line_break_holder] -->        const language = userLang.split('-')[0];<!-- [et_pb_line_break_holder] -->        return translations[language] ? language : 'en'; \/\/ Ingl\u00e9s como fallback<!-- [et_pb_line_break_holder] -->    }<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->    function resolverSistema() {<!-- [et_pb_line_break_holder] -->        const m = [<!-- [et_pb_line_break_holder] -->            [parseFloat(document.getElementById('x1_ec1').value), parseFloat(document.getElementById('y1_ec1').value), parseFloat(document.getElementById('z1_ec1').value), parseFloat(document.getElementById('resultado1').value)],<!-- [et_pb_line_break_holder] -->            [parseFloat(document.getElementById('x2_ec2').value), parseFloat(document.getElementById('y2_ec2').value), parseFloat(document.getElementById('z2_ec2').value), parseFloat(document.getElementById('resultado2').value)],<!-- [et_pb_line_break_holder] -->            [parseFloat(document.getElementById('x3_ec3').value), parseFloat(document.getElementById('y3_ec3').value), parseFloat(document.getElementById('z3_ec3').value), parseFloat(document.getElementById('resultado3').value)]<!-- [et_pb_line_break_holder] -->        ];<!-- [et_pb_line_break_holder] -->        const n = m.length;<!-- [et_pb_line_break_holder] -->        const resultDiv = document.getElementById('result');<!-- [et_pb_line_break_holder] -->        const language = getUserLanguage();<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->        for (let i = 0; i < n; i++) {<!-- [et_pb_line_break_holder] -->            if (isNaN(m[i][0]) || isNaN(m[i][1]) || isNaN(m[i][2]) || isNaN(m[i][3])) {<!-- [et_pb_line_break_holder] -->                resultDiv.innerText = translations[language].errorEntradaInvalida;<!-- [et_pb_line_break_holder] -->                return;<!-- [et_pb_line_break_holder] -->            }<!-- [et_pb_line_break_holder] -->        }<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->        for (let i = 0; i < n; i++) {<!-- [et_pb_line_break_holder] -->            let pivot = m[i][i];<!-- [et_pb_line_break_holder] -->            if (Math.abs(pivot) < 1e-9) {<!-- [et_pb_line_break_holder] -->                resultDiv.innerText = translations[language].errorDeterminanteCero;<!-- [et_pb_line_break_holder] -->                return;<!-- [et_pb_line_break_holder] -->            }<!-- [et_pb_line_break_holder] -->            for (let j = i; j <= n; j++) {<!-- [et_pb_line_break_holder] -->                m[i][j] \/= pivot;<!-- [et_pb_line_break_holder] -->            }<!-- [et_pb_line_break_holder] -->            for (let k = 0; k < n; k++) {<!-- [et_pb_line_break_holder] -->                if (i !== k) {<!-- [et_pb_line_break_holder] -->                    let factor = m[k][i];<!-- [et_pb_line_break_holder] -->                    for (let j = i; j <= n; j++) {<!-- [et_pb_line_break_holder] -->                        m[k][j] -= factor * m[i][j];<!-- [et_pb_line_break_holder] -->                    }<!-- [et_pb_line_break_holder] -->                }<!-- [et_pb_line_break_holder] -->            }<!-- [et_pb_line_break_holder] -->        }<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->        const x = m[0][n].toFixed(2);<!-- [et_pb_line_break_holder] -->        const y = m[1][n].toFixed(2);<!-- [et_pb_line_break_holder] -->        const z = m[2][n].toFixed(2);<!-- [et_pb_line_break_holder] --><!-- [et_pb_line_break_holder] -->        resultDiv.innerText = `${translations[language].solucion} ${x}${translations[language].ySolucion} ${y}${translations[language].zSolucion} ${z}`;<!-- [et_pb_line_break_holder] -->    }<!-- [et_pb_line_break_holder] --><\/script>[\/et_pb_code][et_pb_text admin_label=\u201dVOTE CODE\u201d _builder_version=\u201d4.27.4\u2033 _module_preset=\u201d88b21c46-bab4-4990-9def-73fb03a32482\u2033 text_orientation=\u201dcenter\u201d custom_margin=\u201d0px||0px||true|false\u201d custom_padding=\u201d0px||0px|507px|true|false\u201d custom_padding_tablet=\u201d|||274px|true|false\u201d custom_padding_phone=\u201d|||131px|true|false\u201d custom_padding_last_edited=\u201don|desktop\u201d global_colors_info=\u201d{}\u201d]<\/p>\n<div class=\"et_social_networks et_social_autowidth et_social_slide et_social_circle et_social_top et_social_withcounts et_social_nospace et_social_mobile_on et_social_withnetworknames et_social_outer_dark\">\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t<ul class=\"et_social_icons_container\"><li class=\"et_social_like\">\n\t\t\t\t\t\t<a href=\"#\" class=\"et_social_follow\" data-social_name=\"like\" data-social_type=\"like\" data-post_id=\"0\" target=\"_blank\">\n\t\t\t\t\t\t\t<i class=\"et_social_icon et_social_icon_like\"><\/i>\n\t\t\t\t\t\t\t<div class=\"et_social_network_label\"><div class=\"et_social_networkname\">Vote<\/div><div class=\"et_social_count\">\n\t\t\t\t\t\t<span>0<\/span>\n\t\t\t\t\t\t<span class=\"et_social_count_label\">Likes<\/span>\n\t\t\t\t\t<\/div><\/div>\n\t\t\t\t\t\t\t<span class=\"et_social_overlay\"><\/span>\n\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/li><\/ul>\n\t\t\t\t<\/div>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=\u201d1\u2033 custom_padding_last_edited=\u201don|phone\u201d _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d custom_margin_tablet=\u201d\u201d custom_margin_phone=\u201d\u201d custom_margin_last_edited=\u201don|phone\u201d custom_padding=\u201d0px||||false|false\u201d custom_padding_tablet=\u201d22px||22px||true|false\u201d custom_padding_phone=\u201d22px||22px||true|false\u201d global_colors_info=\u201d{}\u201d][et_pb_row _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d][et_pb_column type=\u201d4_4\u2033 _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d global_colors_info=\u201d{}\u201d][et_pb_text _builder_version=\u201d4.27.4\u2033 _module_preset=\u201ddefault\u201d hover_enabled=\u201d0\u2033 global_colors_info=\u201d{}\u201d sticky_enabled=\u201d0\u2033]<\/p>\n<h2><b>Your Ultimate Tool for Solving Linear Systems<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Are you struggling with complex systems of linear equations? Our Gauss-Jordan Method Calculator offers you step-by-step solutions using matrix reduction. Obtain the values of your unknowns systematically and accurately by transforming the augmented matrix into its reduced echelon form.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Guaranteed Accuracy \u2013 Solve complex linear systems without manual calculation errors.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Step by step (optional) \u2013 Visualize each row operation to understand the reduction process.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Versatile \u2013 Solve systems with multiple equations and unknowns.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Use our calculator now and find solutions to your systems of linear equations in seconds.<\/span><\/p>\n<h2><b>Example of Solving with the Gauss-Jordan Method Calculator<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Imagine you need to solve the following system of linear equations:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">2x+y=7<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x\u2212y=\u22121<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The corresponding augmented matrix is:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">[21\u200b1\u22121\u200b\u2223\u2223\u200b7\u22121\u200b]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Applying the Gauss-Jordan Method (row operations):<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">We swap row 1 and row 2: [12\u200b\u221211\u200b\u2223\u2223\u200b\u221217\u200b]<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">We replace row 2 with F2\u200b\u22122F1\u200b: [10\u200b\u221213\u200b\u2223\u2223\u200b\u221219\u200b]<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">We divide row 2 by 3: [10\u200b\u221211\u200b\u2223\u2223\u200b\u221213\u200b]<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">We replace row 1 with F1\u200b+F2\u200b: [10\u200b01\u200b\u2223\u2223\u200b23\u200b]<\/span><\/li>\n<\/ol>\n<p><b>\ud83d\udcca Result:<\/b><span style=\"font-weight: 400;\"> x=2, y=3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This means that the solution to the system of linear equations is x=2 and y=3.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\ud83d\udce2 Solve your systems of linear equations with our step-by-step calculator.<\/span><\/p>\n<h2><b>How Does Our Gauss-Jordan Method Calculator Work?<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The process is as follows:<\/span><\/p>\n<h3><b>Step 1: Entering the Augmented Matrix<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u270d\ufe0f <\/span><b>Coefficient Matrix:<\/b><span style=\"font-weight: 400;\"> Enter the coefficients of the variables in each equation. Why is this important? They represent the multipliers of your unknowns.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udd22 <\/span><b>Matrix of Independent Terms:<\/b><span style=\"font-weight: 400;\"> Enter the values on the other side of the equal sign in each equation. Why is this important? These are the values at which your equations are equal.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udcd0 The calculator will combine these matrices into the augmented matrix.<\/span><\/li>\n<\/ul>\n<h3><b>Step 2: Application of the Gauss-Jordan Method<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2699\ufe0f The calculator applies a sequence of elementary row operations (row swapping, multiplying a row by a non-zero scalar, adding a multiple of one row to another row) to transform the augmented matrix into its reduced row echelon form.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">(Optional) Some calculators can display each row operation performed.<\/span><\/li>\n<\/ul>\n<h3><b>Step 3: Obtaining the Solution<\/b><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Once the matrix is in reduced echelon form, the solution to the system of equations can be read directly from the last column.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udca1 Each row of the form [1 0 \u2026 0 \u2223 value] corresponds to the solution of one variable.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\ud83d\udce2 Need to solve systems of equations in physics, engineering, or economics? \ud83e\uddd0 Try our calculator for accurate results.<\/span><\/p>\n<h2><b>This is only for entrepreneurs, business owners and freelancers.<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">\ud83d\ude80 If you need to launch your website, SaaS or online store, visit <a href=\"https:\/\/calculatorcch.com\/en\/nippylaunch\/\" title=\"Link to NippyLaunch.com or Nippylaunch.com\" class=\"pretty-link-keyword\"rel=\"\" target=\"_blank\">NippyLaunch.com<\/a>.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\ud83d\udcc8 If you need to do digital advertising and marketing for your company, visit <a href=\"https:\/\/calculatorcch.com\/en\/cleefcompany\/\" title=\"Link to CleefCompany.com or Cleefcompany.com\" class=\"pretty-link-keyword\"rel=\"\" target=\"_blank\">CleefCompany.com<\/a>.<\/span><\/p>\n<h2><b>What is the Gauss-Jordan Method Calculator?<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The Gauss-Jordan Method Calculator is an online tool that implements the Gauss-Jordan algorithm to solve systems of linear equations. This method is based on manipulating the augmented matrix of the system through elementary row operations until the reduced echelon form is obtained. In this form, the solution to the system becomes evident, with each variable isolated in a different row.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This tool is fundamental in linear algebra and has applications in various areas of science, engineering, economics, and computer science to solve problems modeled by systems of linear equations.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\ud83d\udc49 Solve systems of linear equations systematically and reliably with our Gauss-Jordan calculator.<\/span><\/p>\n<h2><b>Recommended books for a deeper understanding of linear algebra and systems of equations<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Explore these readings to help you better understand the fundamentals of linear algebra and solving systems of equations.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">1\ufe0f\u20e3 <\/span><b>\u201cLinear Algebra\u201d by Seymour Lipschutz and Marc Lipson:<\/b><span style=\"font-weight: 400;\"> A complete guide with numerous examples and solved problems.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">2\ufe0f\u20e3 <\/span><b>\u201cIntroduction to Linear Algebra\u201d by Gilbert Strang:<\/b><span style=\"font-weight: 400;\"> A classic text that addresses the concepts of linear algebra in an intuitive way.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">3\ufe0f\u20e3 <\/span><b>\u201cLinear Algebra with Applications\u201d by Gareth Williams:<\/b><span style=\"font-weight: 400;\"> Presents the theory of linear algebra along with its various applications in science and engineering.<\/span><\/p>\n<h2><b>Why Use Our Gauss-Jordan Method Calculator?<\/b><\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Accuracy \u2013 Minimizes errors that can occur in manual calculations.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Efficiency \u2013 Solves complex systems quickly.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Clarity \u2013 (If the calculator offers it) Shows the intermediate steps in the process.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Accessibility \u2013 Available online anytime, anywhere.<\/span><\/li>\n<\/ul>\n<h2><b>Avoid These Common Mistakes When Using the Gauss-Jordan Method Calculator<\/b><\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udeab Incorrectly entering coefficients or independent terms in the matrix.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udeab Not verifying the correct dimension of the entered matrix.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\ud83d\udeab Misinterpreting the solution obtained from the matrix in reduced echelon form.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Use our calculator to solve systems of linear equations with the confidence of obtaining accurate results.<\/span><\/p>\n<h2><b>Comparison: Gauss-Jordan Method Calculator vs. Traditional Methods<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Why use our calculator instead of solving systems manually by substitution, matching, or elimination?<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Systematic \u2013 The Gauss-Jordan method is a systematic algorithm that always leads to the solution (if one exists).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 General \u2013 Works for systems of any size (within the limitations of the calculator).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Less error-prone \u2013 Automates calculations, reducing the possibility of algebraic errors.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u2705 Efficient for large systems \u2013 It becomes more advantageous as the number of equations and unknowns increases.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Solve systems of linear equations efficiently and accurately with our specialized tool.<\/span><\/p>\n<h2><b>Frequently Asked Questions about the Gauss-Jordan Method Calculator<\/b><\/h2>\n<h3><b>What is a system of linear equations?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">It is a set of two or more linear equations with the same unknowns. The objective is to find the values of the unknowns that satisfy all the equations simultaneously.<\/span><\/p>\n<h3><b>What is the augmented matrix?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">It is a matrix that is formed by combining the matrix of coefficients of the system of equations with the matrix of the independent terms, separated by a vertical line (representing the equal sign).<\/span><\/p>\n<h3><b>What is the reduced echelon form of a matrix?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">A matrix is in reduced echelon form if it satisfies the following conditions: the first non-zero element of each row (pivot) is 1, the pivots are in different columns, the pivots appear from top to bottom and from left to right, and all other elements in a pivot&#039;s column are zero.<\/span><\/p>\n<h3><b>Does a system of linear equations always have a solution?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">No, a system of linear equations can have a single solution, infinitely many solutions, or no solutions at all. The Gauss-Jordan method can determine which of these cases exists.<\/span><\/p>\n<h3><b>What if the calculator displays a row of zeros equal to a non-zero number?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">This indicates that the system of equations has no solution (is inconsistent).<\/span><\/p>\n<h3><b>What if the calculator displays rows of zeros at the end of the matrix in reduced row echelon form?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">This indicates that the system has infinite solutions (it is dependent).<\/span><\/p>\n<h3><b>Do I need to know advanced linear algebra to use this calculator?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">No, you just need to be able to correctly enter the augmented matrix of the system of equations. The calculator handles the reduction process.<\/span><\/p>\n<h3><b>Can I solve systems with fractions or decimals as coefficients?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Yes, the calculator should be able to handle coefficients that are rational or real numbers.<\/span><\/p>\n<h3><b>Is there a limit to the number of equations and unknowns I can enter?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">There may be technical limitations depending on the calculator&#039;s implementation. Generally, systems with a reasonable number of variables and equations can be solved.<\/span><\/p>\n<h3><b>Is this tool useful for verifying my manually obtained solutions?<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Absolutely. You can use the calculator to verify the solutions you obtained by solving the system manually using other methods.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Still have questions? Use our calculator and master solving systems of linear equations.<\/span><\/p>\n<p>[\/et_pb_text][et_pb_image src=\u201d@ET-DC@eyJkeW5hbWljIjp0cnVlLCJjb250ZW50IjoicG9zdF9mZWF0dXJlZF9pbWFnZSIsInNldHRpbmdzIjp7fX0=@\u201d alt=\u201dDebt Ratio Calculator\u201d title_text=\u201dDebt Ratio Calculator\u201d align=\u201dcenter\u201d align_tablet=\u201dcenter\u201d align_phone=\u201dcenter\u201d align_last_edited=\u201don|desktop\u201d _builder_version=\u201d4.27.4\u2033 _dynamic_attributes=\u201dsrc\u201d _module_preset=\u201ddefault\u201d custom_margin_tablet=\u201d||30px||false|false\u201d custom_margin_phone=\u201d||30px||false|false\u201d custom_margin_last_edited=\u201don|phone\u201d global_colors_info=\u201d{}\u201d][\/et_pb_image][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>","protected":false},"excerpt":{"rendered":"<p>Solve systems of linear equations efficiently with our Gauss-Jordan method calculator. Enter the coefficient matrix and constant terms to obtain the reduced row echelon form and the solution to the system. Simplify linear algebra!<\/p>","protected":false},"author":5,"featured_media":3690,"parent":3671,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-3764","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages\/3764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/comments?post=3764"}],"version-history":[{"count":2,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages\/3764\/revisions"}],"predecessor-version":[{"id":3766,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages\/3764\/revisions\/3766"}],"up":[{"embeddable":true,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/pages\/3671"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/media\/3690"}],"wp:attachment":[{"href":"https:\/\/calculatorcch.com\/en\/wp-json\/wp\/v2\/media?parent=3764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}