{"id":239633,"date":"2022-05-10T17:08:52","date_gmt":"2022-05-10T15:08:52","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=239633"},"modified":"2025-10-25T12:45:12","modified_gmt":"2025-10-25T10:45:12","slug":"calculer-le-rang-dune-matrice","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/calculer-le-rang-dune-matrice\/","title":{"rendered":"M\u00e9thode : comment calculer le rang d’une matrice ?"},"content":{"rendered":"\n

Avez-vous des difficult\u00e9s \u00e0 calculer le rang d\u2019une matrice<\/strong> ? Si c’est le cas, cet article est fait pour vous ! Nous allons vous guider \u00e0 travers la m\u00e9thode de calcul du rang d’une matrice, une comp\u00e9tence cl\u00e9 en alg\u00e8bre.<\/p>\n

\ud83d\udc69\u200d\ud83c\udfeb En compl\u00e9ment, approfondissez la th\u00e9orie des matrices et leurs applications concr\u00e8tes avec nos cours d’alg\u00e8bre \u00e0 domicile<\/strong><\/a>, sp\u00e9cialement con\u00e7us pour vous accompagner vers la r\u00e9ussite !<\/p>\n\n\n\n

M\u00e9thode : Calculer le rang d’une matrice<\/h2>\n\n\n\n

Conseils m\u00e9thodologiques<\/h3>\n\n\n\n

<\/p>\nPour d\u00e9terminer le rang d’une matrice \"A\" non nulle, on utilise des op\u00e9rations \u00e9l\u00e9mentaires sur les lignes et les colonnes de \"A\" pour montrer que \"A\" est \u00e9quivalente \u00e0 une matrice de la forme :\n

  <\/span>   <\/span>\"\[B=\begin{pmatrix}<\/p>\no\u00f9 les \"r\" coefficients diagonaux \"a_1\", \"...\" , \"a_r\" sont non nuls. On conclut alors que le rang de \"A\" est alors \u00e9gal \u00e0 \"r\".
\nEn effet, \u00e0 l’aide d’op\u00e9rations \u00e9l\u00e9mentaires sur les lignes et colonnes, on peut passer de \"B\" \u00e0 la matrice \"J_r\" qui est de rang \"r\". Donc, \"\mathrm{rg}(A)=\mathrm{rg}(B)=\mathrm{rg}(J_r)=r\".\n\n\n\n

Application de la m\u00e9thode <\/h3>\n\n\n\n

<\/p>\nD\u00e9terminons le rang de \"A=\begin{pmatrix}.\n\nOn a :\n

  <\/span>   <\/span>\"\[\begin{array}{rcll}<\/p>\n\n\n\n

\n
\n
\"livre<\/figure>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n
\n
<\/div>\n
\n

Cet article est extrait de l’ouvrage Maths MPSI-MP2I. Tout-en-un : cours, m\u00e9thodes, entra\u00eenement et corrig\u00e9s <\/em>(\u00e9ditions Vuibert, juin 2021) \u00e9crit par E. Thomas, S. Bellec, G. Boutard. ISBN n\u00b09782311408720<\/em><\/p>\n\n <\/div>\n <\/section>\n<\/div>\n<\/div>\n\n\n

\n \n
\n \n
\n
\n \n\n
<\/div>\n <\/div>\n
\n \n\n
<\/div>\n <\/div>\n
\n \n\n
<\/div>\n <\/div>\n
\n \n\n
<\/div>\n <\/div>\n
\n \n\n
<\/div>\n <\/div>\n <\/div>\n \n
\n
\n \n\n
<\/div>\n <\/div>\n
\n \n\n
<\/div>\n <\/div>\n
\n \n\n
<\/div>\n <\/div>\n
\n \n\n
<\/div>\n <\/div>\n
\n \n\n
<\/div>\n <\/div>\n <\/div>\n<\/div>\n \n\n
\n 3.4\/5 - (5 votes) <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

Avez-vous des difficult\u00e9s \u00e0 calculer le rang d\u2019une matrice ? Si c’est le cas, cet article est fait (…)<\/p>\n","protected":false},"author":158,"featured_media":244645,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":true,"footnotes":""},"category":[803,810],"tag":[78,345],"class_list":["post-239633","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths","tag-prepa","tag-prepa-scientifique"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/239633","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/users\/158"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=239633"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/239633\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/244645"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=239633"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=239633"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=239633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}