{"id":100,"date":"2026-09-28T08:16:43","date_gmt":"2026-09-28T06:16:43","guid":{"rendered":"https:\/\/clases.jesussoto.es\/?p=100"},"modified":"2026-08-20T13:20:55","modified_gmt":"2026-08-20T11:20:55","slug":"alg-operaciones-con-matrices-en-maxima","status":"publish","type":"post","link":"https:\/\/clases.jesussoto.es\/?p=100","title":{"rendered":"ALG: Operaciones con matrices en maxima"},"content":{"rendered":"<h2>Operaciones con matrices en maxima<\/h2>\n<p>El pasado d\u00eda vimos como realizar transformaciones elementales para encontrar una matriz escalonada de cualquier matriz. Estas operaciones son f\u00e1ciles con maxima utilizando estos comandos:<\/p>\n<ul>\n<li><strong>rowswap<\/strong>(\\(M\\), i, j): dada la matriz \\(M\\) nos devuelve la misma donde la se han intercambiado las filas <em>i<\/em> y <em>j<\/em>, \\(f_i\\leftrightarrow f_j\\).<\/li>\n<li><strong>columnswap<\/strong>(\\(M\\), i, j): dada la matriz \\(M\\) nos devuelve la misma donde la se han intercambiado las columnas <em>i<\/em> y <em>j<\/em>, \\(c_i\\leftrightarrow c_j\\).<\/li>\n<\/ul>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Dar las matrices de paso, por la izquierda y por la derecha, que verifica la semejanza \\[\\begin{bmatrix}<br \/>\n0 &#038; 0 &#038; 1 &#038; 2 \\\\<br \/>\n0 &#038; 0 &#038; 2 &#038; 1 \\\\<br \/>\n3 &#038; 4 &#038; 0 &#038; 0 \\\\<br \/>\n4 &#038; 3 &#038; 0 &#038; 0 \\\\<br \/>\n\\end{bmatrix}\\sim \\begin{bmatrix}<br \/>\n0 &#038; 0 &#038; 3 &#038; 4 \\\\<br \/>\n0 &#038; 0 &#038; 4 &#038; 3 \\\\<br \/>\n1 &#038; 2 &#038; 0 &#038; 0 \\\\<br \/>\n2 &#038; 1 &#038; 0 &#038; 0<br \/>\n\\end{bmatrix}\\]\n<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv43() {\n  var htmlShow43 = document.getElementById(\"html-show43\");\n  if (htmlShow43.style.display === \"none\") {\n    htmlShow43.style.display = \"block\";\n  } else {\n    htmlShow43.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv43()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show43\" style=\"display: none;\">\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">A<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">matrix<\/span><span class=\"code_operator\">(<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">4<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">addcol<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">A<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">ident<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}0 &amp; 0 &amp; 1 &amp; 2 &amp; 1 &amp; 0 &amp; 0 &amp; 0\\\\0 &amp; 0 &amp; 2 &amp; 1 &amp; 0 &amp; 1 &amp; 0 &amp; 0\\\\3 &amp; 4 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; 0\\\\4 &amp; 3 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1\\end{bmatrix}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i4)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">rowswap<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">X<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">rowswap<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">X<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}3 &amp; 4 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; 0\\\\4 &amp; 3 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1\\\\0 &amp; 0 &amp; 1 &amp; 2 &amp; 1 &amp; 0 &amp; 0 &amp; 0\\\\0 &amp; 0 &amp; 2 &amp; 1 &amp; 0 &amp; 1 &amp; 0 &amp; 0\\end{bmatrix}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i5)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">EL<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">submatrix<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">X<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}0 &amp; 0 &amp; 1 &amp; 0\\\\0 &amp; 0 &amp; 0 &amp; 1\\\\1 &amp; 0 &amp; 0 &amp; 0\\\\0 &amp; 1 &amp; 0 &amp; 0\\end{bmatrix}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i6)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">addrow<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">submatrix<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">X<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">6<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">7<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">8<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">ident<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}3 &amp; 4 &amp; 0 &amp; 0\\\\4 &amp; 3 &amp; 0 &amp; 0\\\\0 &amp; 0 &amp; 1 &amp; 2\\\\0 &amp; 0 &amp; 2 &amp; 1\\\\1 &amp; 0 &amp; 0 &amp; 0\\\\0 &amp; 1 &amp; 0 &amp; 0\\\\0 &amp; 0 &amp; 1 &amp; 0\\\\0 &amp; 0 &amp; 0 &amp; 1\\end{bmatrix}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i8)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">columnswap<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">X<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">columnswap<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">X<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}0 &amp; 0 &amp; 3 &amp; 4\\\\0 &amp; 0 &amp; 4 &amp; 3\\\\1 &amp; 2 &amp; 0 &amp; 0\\\\2 &amp; 1 &amp; 0 &amp; 0\\\\0 &amp; 0 &amp; 1 &amp; 0\\\\0 &amp; 0 &amp; 0 &amp; 1\\\\1 &amp; 0 &amp; 0 &amp; 0\\\\0 &amp; 1 &amp; 0 &amp; 0\\end{bmatrix}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i9)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">ER<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">submatrix<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">X<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}0 &amp; 0 &amp; 1 &amp; 0\\\\0 &amp; 0 &amp; 0 &amp; 1\\\\1 &amp; 0 &amp; 0 &amp; 0\\\\0 &amp; 1 &amp; 0 &amp; 0\\end{bmatrix}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i10)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">EL<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_variable\">A<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_variable\">ER<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}0 &amp; 0 &amp; 3 &amp; 4\\\\0 &amp; 0 &amp; 4 &amp; 3\\\\1 &amp; 2 &amp; 0 &amp; 0\\\\2 &amp; 1 &amp; 0 &amp; 0\\end{bmatrix}\\]<\/p>\n<\/div>\n<hr \/>\n<ul>\n<li><strong>rowop<\/strong>(\\(M\\), i, j, \\(\\alpha\\)): dada la matriz \\(M\\) nos devuelve la misma donde la \\(f_i\\leftarrow f_i-\\alpha f_j\\).<\/li>\n<li><strong>columnop<\/strong>(\\(M\\), i, j, \\(\\alpha\\)): dada la matriz \\(M\\) nos devuelve la misma donde la \\(c_i\\leftarrow c_i-\\alpha c_j\\).<\/li>\n<\/ul>\n<p>Con estos comandos podemos realizar las operaciones elementales que tratamos en clases anteriores. Sin embargo, una de las operaciones tiene un procedimiento m\u00e1s delicado: la multiplicaci\u00f3n de una fila por un escalar. Imaginemos que el elemento \\(a_{ic}=\\gamma\\) de una matriz queremos que su valor sea \\(\\beta\\), necesitamos saber qu\u00e9 escalar \\(\\alpha\\) debemos multiplicar a la fila \\(f_i\\) para que el comando <strong>rowop<\/strong>(\\(M\\), i, i, \\(\\alpha\\)) transforme \\(a_{ic}=\\gamma\\) en \\(a_{ic}=\\beta\\). Luego \\[\\beta f_i={\\gamma}f_i \\ -\\ {\\gamma}{\\alpha}f_i\\to \\alpha=1-\\frac{\\beta}{\\gamma}.\\]<br \/>\nDe esta forma, solo necesitamos sustituir para encontrar el \\(\\alpha\\) apropiado que nos proporcione \\(\\beta\\).<\/p>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Dada \\(\\begin{bmatrix}2 &#038; \\operatorname{-}4 &#038; 3\\\\ 6 &#038; \\operatorname{-}8 &#038; 5\\\\ 6 &#038; 1 &#038; 7\\end{bmatrix}\\). Encontrar una matriz triangular superior que sea semejante por operaciones elementales.<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv63() {\n  var htmlShow63 = document.getElementById(\"html-show63\");\n  if (htmlShow63.style.display === \"none\") {\n    htmlShow63.style.display = \"block\";\n  } else {\n    htmlShow63.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv63()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show63\" style=\"display: none;\">\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">A<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">matrix<\/span><span class=\"code_operator\">(<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">4<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">6<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">8<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">5<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">6<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">7<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">addcol<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">ident<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">A<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}2 &amp; -4 &amp; 3\\\\6 &amp; -8 &amp; 5\\\\6 &amp; 1 &amp; 7\\end{bmatrix}\\]<\/p>\n<p>\\[\\begin{bmatrix}1 &amp; 0 &amp; 0 &amp; 2 &amp; -4 &amp; 3\\\\0 &amp; 1 &amp; 0 &amp; 6 &amp; -8 &amp; 5\\\\0 &amp; 0 &amp; 1 &amp; 6 &amp; 1 &amp; 7\\end{bmatrix}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i3)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">rowop<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">X<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}1 &amp; 0 &amp; 0 &amp; 2 &amp; -4 &amp; 3\\\\-3 &amp; 1 &amp; 0 &amp; 0 &amp; 4 &amp; -4\\\\0 &amp; 0 &amp; 1 &amp; 6 &amp; 1 &amp; 7\\end{bmatrix}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i4)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">rowop<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">X<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}1 &amp; 0 &amp; 0 &amp; 2 &amp; -4 &amp; 3\\\\-3 &amp; 1 &amp; 0 &amp; 0 &amp; 4 &amp; -4\\\\-3 &amp; 0 &amp; 1 &amp; 0 &amp; 13 &amp; -2\\end{bmatrix}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i5)\t<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">X<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">rowop<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">X<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">13<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\begin{bmatrix}1 &amp; 0 &amp; 0 &amp; 2 &amp; -4 &amp; 3\\\\-3 &amp; 1 &amp; 0 &amp; 0 &amp; 4 &amp; -4\\\\\\frac{27}{4} &amp; -\\frac{13}{4} &amp; 1 &amp; 0 &amp; 0 &amp; 11\\end{bmatrix}\\]<\/p>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Dada la matriz propuesta en el video, realizar las mismas operaciones con maxima para concluir con la matriz escalonada que proporciona.<br \/>\n<iframe loading=\"lazy\" title=\"\u00c1lgebra Lineal - Matrices Semejantes por Transformaciones Elementales. Ej.3 - Jes\u00fas Soto\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/ut2WSWWbAJ8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/p>\n<\/blockquote>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Realizar como anteriormente con la matriz dada en:<br \/>\n<iframe loading=\"lazy\" title=\"\u00c1lgebra Lineal - Matrices semejantes por transformaciones elementales Ej.1 - Jes\u00fas Soto\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/V3-ghD34poQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/p>\n<\/blockquote>\n<hr \/>\n<h2>Rango de una matriz<\/h2>\n<p>Tenemos una funci\u00f3n que nos permite calcular el rango de una matriz:<\/p>\n<ul>\n<li><strong>rank<\/strong>(<em>M<\/em>): Calcula el rango de la matriz <em>M<\/em>.<\/li>\n<\/ul>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Verifica el resultado del ejercicio<br \/>\n<iframe loading=\"lazy\" title=\"\u00c1lgebra Lineal - Rango de una matriz. Ej. 1 - Jes\u00fas Soto\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/iVSfMe8G8uA?start=9&amp;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/p>\n<\/blockquote>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Sea A:[[1,2,-3], [-2,0,4], [0,4,-2], [-2,-4,<strong>a<\/strong>]]. \u00bfCu\u00e1l es el valor de <strong>a<\/strong> para que el rango de la matriz sea par?<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv63f2() {\n  var htmlShow63f2 = document.getElementById(\"html-show63f2\");\n  if (htmlShow63f2.style.display === \"none\") {\n    htmlShow63f2.style.display = \"block\";\n  } else {\n    htmlShow63f2.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv63f2()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show63f2\" style=\"display: none;\">\n<iframe loading=\"lazy\" title=\"\u00c1lgebra Lineal - Rango de una matriz. Ej.5 - Jes\u00fas Soto\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/BY_dkD06MYY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Sea A:[[1,<strong>a<\/strong>,<strong>b<\/strong>,0], [2,2<strong>a<\/strong>,<strong>b<\/strong>,1], [2,3,<strong>b<\/strong>,0], [0,1,0,1]], con <strong>a<\/strong>,<strong>b<\/strong>\\(\\in\\mathbb{R}\\). \u00bfCu\u00e1l es el rango de la matriz seg\u00fan los par\u00e1metros dados?<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv63f21() {\n  var htmlShow63f21 = document.getElementById(\"html-show63f21\");\n  if (htmlShow63f21.style.display === \"none\") {\n    htmlShow63f21.style.display = \"block\";\n  } else {\n    htmlShow63f21.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv63f21()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show63f21\" style=\"display: none;\">\n<iframe loading=\"lazy\" title=\"\u00c1lgebra Lineal - Rango de una matriz. Ej. 6 - Jes\u00fas Soto\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/AAX_Z9JB1ok?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div>\n<hr \/>\n","protected":false},"excerpt":{"rendered":"<p>Operaciones con matrices en maxima El pasado d\u00eda vimos como realizar transformaciones elementales para encontrar una matriz escalonada de cualquier matriz. Estas operaciones son f\u00e1ciles con maxima utilizando estos comandos: rowswap(\\(M\\), i,&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[20],"class_list":["post-100","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-practicas-algebra"],"_links":{"self":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=100"}],"version-history":[{"count":3,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/100\/revisions"}],"predecessor-version":[{"id":103,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/100\/revisions\/103"}],"wp:attachment":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}