{"id":742,"date":"2026-10-03T05:52:19","date_gmt":"2026-10-03T02:52:19","guid":{"rendered":"https:\/\/wpcalc.com\/fr\/?p=742"},"modified":"2026-10-03T05:52:19","modified_gmt":"2026-10-03T02:52:19","slug":"somme-des-determinants","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/fr\/mathematiques\/somme-des-determinants\/","title":{"rendered":"Calculateur de somme de d\u00e9terminants"},"content":{"rendered":"<p><section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Outil de calcul de la somme des d\u00e9terminants<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"742\" data-favorite-title=\"Somme de d\u00e9terminants\" data-favorite-url=\"https:\/\/wpcalc.com\/fr\/mathematiques\/somme-des-determinants\/\" data-favorite-excerpt=\"Saisissez les coefficients de deux matrices carr\u00e9es (2 \u00d7 2 ou 3 \u00d7 3) et ce calculateur d\u00e9termine les deux d\u00e9terminants ainsi que leur somme |A| + |B| instantan\u00e9ment, avec les formules expliqu\u00e9es \u00e9tape par \u00e9tape.\" aria-label=\"Ajouter aux favoris\" data-favorite-icon=\"icon icon-binary\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/fr\/mathematiques\/somme-des-determinants\/\" method=\"POST\" class=\"calculator\" id=\"calculator-742\" data-post=\"742\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Champs de saisie<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Taille de la matrice<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"taille_de_la_matrice\"><option value=\"2\">2 \u00d7 2<\/option><option value=\"3\">3 \u00d7 3<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"is-single field\" id=\"input-2\"><span class=\"font-semibold\">Matrice A<\/span><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">a\u2081\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-3\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">a\u2081\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-4\" step=\"any\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-5\" hidden><label for=\"field-5\">a\u2081\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-5\" step=\"any\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-6\"><label for=\"field-6\">a\u2082\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-6\" step=\"any\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-7\"><label for=\"field-7\">a\u2082\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-7\" step=\"any\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-8\" hidden><label for=\"field-8\">a\u2082\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-8\" step=\"any\" value=\"6\"\/><\/div><div class=\"field\" id=\"input-9\" hidden><label for=\"field-9\">a\u2083\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-9\" step=\"any\" value=\"7\"\/><\/div><div class=\"field\" id=\"input-10\" hidden><label for=\"field-10\">a\u2083\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-10\" step=\"any\" value=\"8\"\/><\/div><div class=\"field\" id=\"input-11\" hidden><label for=\"field-11\">a\u2083\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-11\" step=\"any\" value=\"9\"\/><\/div><div class=\"is-single field\" id=\"input-12\"><span class=\"font-semibold\">Matrice B<\/span><\/div><div class=\"field\" id=\"input-13\"><label for=\"field-13\">b\u2081\u2081<\/label><input type=\"number\" name=\"b\" id=\"field-13\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-14\"><label for=\"field-14\">b\u2081\u2082<\/label><input type=\"number\" name=\"b\" id=\"field-14\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-15\" hidden><label for=\"field-15\">b\u2081\u2083<\/label><input type=\"number\" name=\"b\" id=\"field-15\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-16\"><label for=\"field-16\">b\u2082\u2081<\/label><input type=\"number\" name=\"b\" id=\"field-16\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-17\"><label for=\"field-17\">b\u2082\u2082<\/label><input type=\"number\" name=\"b\" id=\"field-17\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-18\" hidden><label for=\"field-18\">b\u2082\u2083<\/label><input type=\"number\" name=\"b\" id=\"field-18\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-19\" hidden><label for=\"field-19\">b\u2083\u2081<\/label><input type=\"number\" name=\"b\" id=\"field-19\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-20\" hidden><label for=\"field-20\">b\u2083\u2082<\/label><input type=\"number\" name=\"b\" id=\"field-20\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-21\" hidden><label for=\"field-21\">b\u2083\u2083<\/label><input type=\"number\" name=\"b\" id=\"field-21\" step=\"any\" value=\"1\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalculer\" id=\"calculate-button\" data-post=\"742\">Calculer<\/button><button type=\"reset\">R\u00e9initialiser<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculer automatiquement<\/label><small>Si activ\u00e9, le r\u00e9sultat se met \u00e0 jour automatiquement d\u00e8s que vous modifiez une valeur.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Vos r\u00e9sultats<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>|A|<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>|B|<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>|A| + |B|<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copier le lien vers ce calcul<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Laisser un commentaire<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"742\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Que pensez-vous de ce r\u00e9sultat\u00a0?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">J\u2019aime <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Utile <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confus <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">D\u00e9\u00e7u <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inexact <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div><br \/>\n<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Somme de d\u00e9terminants \u2013 Exemple de calcul<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"742\" data-favorite-title=\"Somme de d\u00e9terminants\" data-favorite-url=\"https:\/\/wpcalc.com\/fr\/mathematiques\/somme-des-determinants\/\" data-favorite-excerpt=\"Saisissez les coefficients de deux matrices carr\u00e9es (2 \u00d7 2 ou 3 \u00d7 3) et ce calculateur d\u00e9termine les deux d\u00e9terminants ainsi que leur somme |A| + |B| instantan\u00e9ment, avec les formules expliqu\u00e9es \u00e9tape par \u00e9tape.\" aria-label=\"Ajouter aux favoris\" data-favorite-icon=\"icon icon-binary\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/fr\/mathematiques\/somme-des-determinants\/\" method=\"POST\" class=\"calculator\" id=\"calculator-742\" data-post=\"742\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Champs de saisie<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Montant du premier pr\u00eat<\/label><div class=\"term\">L1<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"montant_du_premier_prt\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"100000\"\/><div class=\"unit\" id=\"calc-unit-1\">$<\/div><small id=\"calc-info-1\">Saisissez le montant du premier pr\u00eat<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Taux d\u2019int\u00e9r\u00eat du premier pr\u00eat<\/label><div class=\"term\">r1<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"taux_dintrt_du_premier_prt\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" max=\"100\" value=\"4\"\/><div class=\"unit\" id=\"calc-unit-2\">%<\/div><small id=\"calc-info-2\">Saisissez le taux d\u2019int\u00e9r\u00eat du premier pr\u00eat<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Montant du second pr\u00eat<\/label><div class=\"term\">L2<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"montant_du_second_prt\" id=\"field-3\" aria-describedby=\"calc-unit-3 calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"50000\"\/><div class=\"unit\" id=\"calc-unit-3\">$<\/div><small id=\"calc-info-3\">Saisissez le montant du second pr\u00eat<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Taux d\u2019int\u00e9r\u00eat du second pr\u00eat<\/label><div class=\"term\">r2<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"taux_dintrt_du_second_prt\" id=\"field-4\" aria-describedby=\"calc-unit-4 calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" max=\"100\" value=\"6\"\/><div class=\"unit\" id=\"calc-unit-4\">%<\/div><small id=\"calc-info-4\">Saisissez le taux d\u2019int\u00e9r\u00eat du second pr\u00eat<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalculer\" id=\"calculate-button\" data-post=\"742\">Calculer<\/button><button type=\"reset\">R\u00e9initialiser<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculer automatiquement<\/label><small>Si activ\u00e9, le r\u00e9sultat se met \u00e0 jour automatiquement d\u00e8s que vous modifiez une valeur.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Vos r\u00e9sultats<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Taux d\u2019int\u00e9r\u00eat pond\u00e9r\u00e9<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"%\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copier le lien vers ce calcul<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Laisser un commentaire<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"742\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Que pensez-vous de ce r\u00e9sultat\u00a0?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">J\u2019aime <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Utile <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confus <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">D\u00e9\u00e7u <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inexact <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div><\/p>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Formule de la somme des d\u00e9terminants<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formule<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ |A| + |B| = \\det(A) + \\det(B) \\]\n\\[ \\det\\!\\begin{bmatrix} a &amp; b \\\\ c &amp; d \\end{bmatrix} = ad - bc \\]\n\\[ \\det\\!\\begin{bmatrix} a_{11} &amp; a_{12} &amp; a_{13} \\\\ a_{21} &amp; a_{22} &amp; a_{23} \\\\ a_{31} &amp; a_{32} &amp; a_{33} \\end{bmatrix} = a_{11}(a_{22}a_{33} - a_{23}a_{32}) - a_{12}(a_{21}a_{33} - a_{23}a_{31}) + a_{13}(a_{21}a_{32} - a_{22}a_{31}) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>O\u00f9&nbsp;:<\/strong><\/p>\n<ul>\n<li>\\(A\\) et \\(B\\) \u2014 matrices carr\u00e9es de m\u00eame taille (2 \u00d7 2 ou 3 \u00d7 3)<\/li>\n<li>\\(\\det(A)\\), not\u00e9 \\(|A|\\) \u2014 le d\u00e9terminant de la matrice \\(A\\)<\/li>\n<li>\\(\\det(B)\\), not\u00e9 \\(|B|\\) \u2014 le d\u00e9terminant de la matrice \\(B\\)<\/li>\n<\/ul>\n<p>La premi\u00e8re ligne \u00e9nonce l'op\u00e9ration elle-m\u00eame : chaque d\u00e9terminant est calcul\u00e9 ind\u00e9pendamment, puis les deux r\u00e9sultats scalaires sont additionn\u00e9s. La deuxi\u00e8me et la troisi\u00e8me ligne montrent comment un d\u00e9terminant unique est \u00e9valu\u00e9 pour des matrices 2 \u00d7 2 et 3 \u00d7 3 (d\u00e9veloppement par cofacteurs selon la premi\u00e8re ligne).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Somme de d\u00e9terminants \u2013 Exemple de calcul<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemple&nbsp;:<\/strong> deux matrices 3 \u00d7 3 avec les valeurs par d\u00e9faut du calculateur&nbsp;:<\/p>\n<p>\\[ A = \\begin{bmatrix} 1 &amp; 2 &amp; 3 \\\\ 4 &amp; 5 &amp; 6 \\\\ 7 &amp; 8 &amp; 9 \\end{bmatrix}, \\quad B = \\begin{bmatrix} 1 &amp; 0 &amp; 0 \\\\ 0 &amp; 1 &amp; 0 \\\\ 0 &amp; 0 &amp; 1 \\end{bmatrix} \\]<\/p>\n<p>\\[ \\det(A) = 1(5 \\cdot 9 - 6 \\cdot 8) - 2(4 \\cdot 9 - 6 \\cdot 7) + 3(4 \\cdot 8 - 5 \\cdot 7) = 1(-3) - 2(-6) + 3(-3) = -3 + 12 - 9 = 0 \\]<\/p>\n<p>\\[ \\det(B) = 1(1 \\cdot 1 - 0 \\cdot 0) - 0(0 \\cdot 1 - 0 \\cdot 0) + 0(0 \\cdot 0 - 1 \\cdot 0) = 1 \\]<\/p>\n<p>\\[ |A| + |B| = 0 + 1 = 1 \\]<\/p>\n<p><strong>R\u00e9sultat&nbsp;:<\/strong> \\(\\det(A) = 0\\), \\(\\det(B) = 1\\), et la somme des d\u00e9terminants vaut \\(1\\). Notez que la matrice \\(A\\) est singuli\u00e8re (ses lignes sont lin\u00e9airement d\u00e9pendantes), c'est pourquoi son d\u00e9terminant est nul.<\/p>\n<p>\n\r\n<\/section>\n<h2>Comment utiliser le calculateur<\/h2>\n<ol>\n<li>S\u00e9lectionnez la <strong>taille de matrice<\/strong> \u2014 2 \u00d7 2 ou 3 \u00d7 3 \u2014 dans le menu d\u00e9roulant en haut. Les champs 3 \u00d7 3 apparaissent ou se masquent automatiquement.<\/li>\n<li>Saisissez les coefficients de la <strong>matrice A<\/strong> dans les champs \u00e9tiquet\u00e9s a\u2081\u2081 \u00e0 a\u2083\u2083 (ligne par ligne).<\/li>\n<li>Saisissez les coefficients de la <strong>matrice B<\/strong> dans les champs \u00e9tiquet\u00e9s b\u2081\u2081 \u00e0 b\u2083\u2083.<\/li>\n<li>Les r\u00e9sultats se mettent \u00e0 jour instantan\u00e9ment&nbsp;: <strong>|A|<\/strong>, <strong>|B|<\/strong> et la somme <strong>|A| + |B|<\/strong>.<\/li>\n<\/ol>\n<h2>Qu'est-ce que la somme des d\u00e9terminants&nbsp;?<\/h2>\n<p>Un d\u00e9terminant est un nombre unique calcul\u00e9 \u00e0 partir d'une matrice carr\u00e9e. Il encode des propri\u00e9t\u00e9s cl\u00e9s de la transformation lin\u00e9aire que la matrice repr\u00e9sente : si la transformation est inversible, par quel facteur elle multiplie les aires ou les volumes, et comment elle oriente l'espace. Un d\u00e9terminant nul signifie que la matrice est singuli\u00e8re \u2014 elle aplatit l'espace et n'a pas d'inverse.<\/p>\n<p>La somme des d\u00e9terminants est simplement l'addition scalaire \\(\\det(A) + \\det(B)\\). Chaque matrice est \u00e9valu\u00e9e s\u00e9par\u00e9ment, et seuls les deux nombres obtenus sont combin\u00e9s. C'est un exercice courant en cours d'alg\u00e8bre lin\u00e9aire, et on le retrouve dans des d\u00e9monstrations et des formules o\u00f9 les d\u00e9terminants de plusieurs matrices doivent \u00eatre combin\u00e9s \u2014 par exemple, pour v\u00e9rifier une d\u00e9pendance lin\u00e9aire, \u00e9valuer des expressions de matrices par blocs ou combiner des polyn\u00f4mes caract\u00e9ristiques.<\/p>\n<p>Un point crucial&nbsp;: <strong>la somme des d\u00e9terminants n'est g\u00e9n\u00e9ralement pas \u00e9gale au d\u00e9terminant de la somme<\/strong>. En symboles, \\(\\det(A + B) \\neq \\det(A) + \\det(B)\\) dans presque tous les cas. Le d\u00e9terminant est une fonction non lin\u00e9aire et multiplicative \u2014 il v\u00e9rifie \\(\\det(AB) = \\det(A)\\,\\det(B)\\), ce que vous pouvez v\u00e9rifier avec notre calculateur <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/produit-determinants\/\">Multiplication de d\u00e9terminants<\/a> \u2014 mais il ne se distribue pas sur l'addition matricielle. Si vous avez besoin du d\u00e9terminant de \\(A + B\\), additionnez d'abord les matrices \u00e9l\u00e9ment par \u00e9l\u00e9ment avec le calculateur <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/addition-de-deux-matrices\/\">Addition de matrices<\/a>, puis calculez le d\u00e9terminant du r\u00e9sultat.<\/p>\n<p>L'interpr\u00e9tation du r\u00e9sultat est simple&nbsp;: <strong>|A|<\/strong> et <strong>|B|<\/strong> sont les deux d\u00e9terminants individuels, et <strong>|A| + |B|<\/strong> est leur somme arithm\u00e9tique ordinaire, qui peut \u00eatre positive, n\u00e9gative ou nulle. Une somme nulle n'implique pas qu'une des matrices soit singuli\u00e8re \u2014 un d\u00e9terminant peut simplement annuler l'autre.<\/p>\n<h2>Hypoth\u00e8ses, limites et conseils<\/h2>\n<ul>\n<li><strong>Matrices carr\u00e9es de m\u00eame taille uniquement.<\/strong> Les d\u00e9terminants ne sont d\u00e9finis que pour des matrices carr\u00e9es, et cet outil accepte des matrices 2 \u00d7 2 et 3 \u00d7 3. Les deux matrices n'ont pas besoin d'\u00eatre li\u00e9es d'une autre mani\u00e8re.<\/li>\n<li><strong>Les signes comptent.<\/strong> Le d\u00e9terminant peut \u00eatre n\u00e9gatif. \u00c9changer deux lignes ou deux colonnes change le signe, donc v\u00e9rifiez bien l'ordre dans lequel vous saisissez les valeurs (d'abord la ligne, puis la colonne&nbsp;: a\u2082\u2081 est la ligne 2, colonne 1).<\/li>\n<li><strong>Arrondi.<\/strong> Le calculateur arrondit les r\u00e9sultats affich\u00e9s ; des coefficients tr\u00e8s grands ou des nombres comportant de nombreuses d\u00e9cimales peuvent donc perdre un peu de pr\u00e9cision dans le r\u00e9sultat affich\u00e9.<\/li>\n<li><strong>Matrices singuli\u00e8res.<\/strong> Si un d\u00e9terminant vaut 0, la matrice n'a pas d'inverse et ses lignes (et colonnes) sont lin\u00e9airement d\u00e9pendantes. Pour en savoir plus sur une telle matrice, essayez le calculateur <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/rang-matrice-3x3\/\">Rang d'une matrice 3\u00d73<\/a> ou le calculateur <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/calculateur-inverse-matrice-3x3\/\">Matrice inverse 3\u00d73<\/a>.<\/li>\n<li><strong>Vous cherchez plut\u00f4t une soustraction&nbsp;?<\/strong> Pour la diff\u00e9rence \\(\\det(A) - \\det(B)\\), vous pouvez saisir \\(-B\\) comme seconde matrice, puisque \\(\\det(-B) = -\\det(B)\\) pour une 3 \u00d7 3 (et, plus g\u00e9n\u00e9ralement, \\(\\det(-B) = (-1)^n\\det(B)\\) pour une matrice \\(n \\times n\\)). La soustraction de matrices \u00e9l\u00e9ment par \u00e9l\u00e9ment est prise en charge par notre calculateur <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/soustraction-matrices\/\">Soustraction de deux matrices<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Saisissez les coefficients de deux matrices carr\u00e9es (2 \u00d7 2 ou 3 \u00d7 3) et ce calculateur d\u00e9termine les deux d\u00e9terminants ainsi que leur somme |A| + |B| instantan\u00e9ment, avec les formules expliqu\u00e9es \u00e9tape par \u00e9tape.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[24],"class_list":["post-742","post","type-post","status-publish","format-standard","hentry","category-mathematiques","tag-matrices"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/742","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/comments?post=742"}],"version-history":[{"count":7,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/742\/revisions"}],"predecessor-version":[{"id":5241,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/742\/revisions\/5241"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/media?parent=742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/categories?post=742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/tags?post=742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}