{"id":69,"date":"2025-10-07T15:15:28","date_gmt":"2025-10-07T13:15:28","guid":{"rendered":"https:\/\/clases.jesussoto.es\/?p=69"},"modified":"2025-10-05T18:01:36","modified_gmt":"2025-10-05T16:01:36","slug":"mathbio-algebra-con-maxima","status":"publish","type":"post","link":"https:\/\/clases.jesussoto.es\/?p=69","title":{"rendered":"MathBio: \u00c1lgebra con Maxima"},"content":{"rendered":"<p>Hoy nos iniciamos en un sistema para la manipulaci\u00f3n de expresiones simb\u00f3licas y num\u00e9ricas, Maxima. Un herramienta inform\u00e1tica que nos ayudar\u00e1 a resolver problemas de la asignatura de forma sencilla y aplicada.<\/p>\n<p>Para comenzar nos iniciaremos en la definici\u00f3n de vectores y matrices, y las operaciones que podemos hacer con ellos.<\/p>\n<h2>Vectores<\/h2>\n<p>Un vector se define utilizando [] y los elementos del vector separados por comas. Con los vectores podemos hacer las operaciones b\u00e1sicas de suma y multiplicaci\u00f3n por escalar.<\/p>\n<p><code><br \/>\nv:[1,2,3];<br \/>\n3.v+(-2).u;<\/p>\n<p><\/code><\/p>\n<blockquote>\n<p><strong>Ejercicio:<\/strong>  Sean los vectores \\(\\mathbf{u}=[2,-1,5,0]\\), \\(\\mathbf{v}=[4,3,1,-1]\\) y \\(\\mathbf{w}=[-6,2,0,3]\\). Si \\(\\mathbf{x}+\\mathbf{v}+3\\mathbf{w}=2\\mathbf{u}\\), \u00bfcu\u00e1nto suman las coordenadas de \\(\\mathbf{x}\\)? <\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv3() {\n  var htmlShow3 = document.getElementById(\"html-show3\");\n  if (htmlShow3.style.display === \"none\") {\n    htmlShow3.style.display = \"block\";\n  } else {\n    htmlShow3.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv3()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show3\" style=\"display: none;\">\n<p><iframe loading=\"lazy\" src=\"https:\/\/uploads.jesussoto.es\/maxima\/ejrALGvectores01.html\" width=\"650\" height=\"300\" allow=\"fullscreen\"><\/iframe>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Sean los vectores \\(u\\)=[2,-1], \\(u\\)=[1,1] y \\(w\\)=[-1,3], \u00bfcu\u00e1nto es \\(\\textbf{proy}_{w}(u)\\bullet\\textbf{proy}_{w}(v)\\)? <\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv3dx() {\n  var htmlShow3dx = document.getElementById(\"html-show3dx\");\n  if (htmlShow3dx.style.display === \"none\") {\n    htmlShow3dx.style.display = \"block\";\n  } else {\n    htmlShow3dx.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv3dx()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show3dx\" style=\"display: none;\">\n <!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i6) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">u<\/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\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">v<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">w<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">[<\/span><span class=\"code_operator\">\u2212<\/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\">uw<\/span><span class=\"code_operator\">:<\/span><span class=\"code_variable\">u<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_variable\">w<\/span><span class=\"code_endofline\">;<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">vw<\/span><span class=\"code_operator\">:<\/span><span class=\"code_variable\">v<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_variable\">w<\/span><span class=\"code_endofline\">;<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">ww<\/span><span class=\"code_operator\">:<\/span><span class=\"code_variable\">w<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_variable\">w<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }-5\\]<\/p>\n<p>\\[\\operatorname{ }2\\]<\/p>\n<p>\\[\\operatorname{ }10\\]<\/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\">(%i7) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_operator\">(<\/span><span class=\"code_variable\">uw<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_variable\">ww<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">w<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">vw<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_variable\">ww<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">w<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }-1\\]<\/p>\n<\/div>\n<hr \/>\n<h2>Matrices<\/h2>\n<p>Si queremos utilizar matrices nos bastar\u00e1 con definirla mediante <strong>matrix()<\/strong>. Las filas de definimos como vectores:<\/p>\n<p><code><br \/>\nA:matrix([1,2,3],[4,5,6]);<br \/>\nB:matrix([1,2],[3,4],[5,6]);<\/p>\n<p><\/code><\/p>\n<p>La primera, A, ser\u00eda una matriz de 2&#215;3, B ser\u00eda una matriz de 3&#215;2. La manera de acceder a los elementos es mediante A[i,j].<\/p>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Sea \\(A\\)=[[4,-1,6],[2,1,6],[2,-1,8]] y \\(B\\)=[[0,-1,5],[1,6,2],[1,8,0]]. \u00bfCu\u00e1l es la suma de los elementos de la diagonal principal de \\(2A-3B\\)? <\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv23() {\n  var htmlShow23 = document.getElementById(\"html-show23\");\n  if (htmlShow23.style.display === \"none\") {\n    htmlShow23.style.display = \"block\";\n  } else {\n    htmlShow23.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv23()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show23\" style=\"display: none;\">\n<!-- Code cell --> <\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"> <span class=\"prompt\">(%i4) <\/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_number\">4<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>,<span class=\"code_number\">6<\/span>],[<span class=\"code_number\">2<\/span>,<span class=\"code_number\">1<\/span>,<span class=\"code_number\">6<\/span>],[<span class=\"code_number\">2<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>,<span class=\"code_number\">8<\/span>])<span class=\"code_endofline\">$<\/span><br \/><span class=\"code_variable\">B<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">matrix<\/span>([<span class=\"code_number\">0<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>,<span class=\"code_number\">5<\/span>],[<span class=\"code_number\">1<\/span>,<span class=\"code_number\">6<\/span>,<span class=\"code_number\">2<\/span>],[<span class=\"code_number\">1<\/span>,<span class=\"code_number\">8<\/span>,<span class=\"code_number\">0<\/span>])<span class=\"code_endofline\">$<\/span><br \/><span class=\"code_variable\">C<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">*<\/span><span class=\"code_variable\">A<\/span><span class=\"code_operator\">&#8211;<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">*<\/span><span class=\"code_variable\">B<\/span><span class=\"code_endofline\">;<\/span><br \/><span class=\"code_variable\">C<\/span>[<span class=\"code_number\">1<\/span>,<span class=\"code_number\">1<\/span>]<span class=\"code_operator\">+<\/span><span class=\"code_variable\">C<\/span>[<span class=\"code_number\">2<\/span>,<span class=\"code_number\">2<\/span>]<span class=\"code_operator\">+<\/span><span class=\"code_variable\">C<\/span>[<span class=\"code_number\">3<\/span>,<span class=\"code_number\">3<\/span>]<span class=\"code_endofline\">;<\/span> <\/span>  <\/td>\n<\/tr>\n<\/table>\n<p> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable>  <mlabeledtr columnalign=\"center\"> <mtd><mtext>(C)<\/mtext> <\/mtd> <mtd><mrow>  <mo>[<\/mo>  <mrow> <mtable><mtr>  <mtd> <mn>8<\/mn>  <\/mtd>  <mtd> <mn>1<\/mn>  <\/mtd>  <mtd> <mrow><mi>\u2212<\/mi><mn>3<\/mn> <\/mrow>  <\/mtd><\/mtr><mtr>  <mtd> <mn>1<\/mn>  <\/mtd>  <mtd> <mrow><mi>\u2212<\/mi><mn>16<\/mn> <\/mrow>  <\/mtd>  <mtd> <mn>6<\/mn>  <\/mtd><\/mtr><mtr>  <mtd> <mn>1<\/mn>  <\/mtd>  <mtd> <mrow><mi>\u2212<\/mi><mn>26<\/mn> <\/mrow>  <\/mtd>  <mtd> <mn>16<\/mn>  <\/mtd><\/mtr> <\/mtable>  <\/mrow>  <mo>]<\/mo><\/mrow> <\/mtd>  <\/mlabeledtr><\/mtable> <\/math> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable>  <mlabeledtr columnalign=\"center\"> <mtd><mtext>(%o4) <\/mtext> <\/mtd> <mtd><mn>8<\/mn> <\/mtd>  <\/mlabeledtr><\/mtable> <\/math>\n<\/div>\n<hr \/>\n<p>Otros comandos:<\/p>\n<ul>\n<li><strong>col<\/strong>((<em>Matriz<\/em>,<em>N\u00famColumna<\/em>)): Recupera la columna <em>N\u00famColumna<\/em>. <\/li>\n<li><strong>row<\/strong>((<em>Matriz<\/em>,<em>N\u00famFila<\/em>)): Recupera la fila <em>N\u00famFila<\/em>. <\/li>\n<li><strong>submatrix<\/strong>(\\(i_1,i_2,\\ldots,i_p\\), <em>Matriz<\/em>,\\(j_1,j_2,\\ldots,j_q\\)): Elimina de la <em>Matriz <\/em>las filas cuyos n\u00fameros son \\(i_1,i_2,\\ldots,i_p\\) y las columnas cuyos n\u00fameros son \\(j_1,j_2,\\ldots,j_q\\). No es preciso que est\u00e9n ambas: pueden eliminarse \u00fanicamente filas o columnas.<\/li>\n<li><strong>addrow<\/strong>(<em>Matriz<\/em>, \\(v_1, \\ldots, v_p\\)): A\u00f1ade en la base de <em>Matriz <\/em>las filas dadas por vectores (o matrices) \\(v_1, \\ldots, v_p\\). Las longitudes deben ser concordantes.<\/li>\n<li><strong>addcol<\/strong>(<em>Matriz<\/em>, \\(v_1, \\ldots, v_p\\)): A\u00f1ade en la base de <em>Matriz <\/em>las filas dadas por vectores (o matrices) \\(v_1, \\ldots, v_p\\). Las longitudes deben ser concordantes.<\/li>\n<li><strong>matrix_size<\/strong>(<em>Matriz<\/em>): Proporciona las dimensiones de la matriz.<\/li>\n<li><strong>transpose<\/strong>(<em>Matriz<\/em>): Proporciona la matriz traspuesta de <em>Matriz<\/em>.<\/li>\n<\/ul>\n<p>Las operaciones con matrices son semejantes a las utilizadas con los vectores.<\/p>\n<p>Algunas matrices interesantes:<\/p>\n<ul>\n<li><strong>diagmatrix<\/strong>(<em>N\u00famero<\/em>,<em>Valor<\/em>): Genera una matriz cuadrada diagonal cuyo tama\u00f1o se establece mediante el valor de <em>N\u00famero <\/em> y en la que todos los elementos de la diagonal tienen el mismo <em>Valor<\/em>. <\/li>\n<li><strong>diag_matrix<\/strong>(\\(a_1,a_2,\\ldots,a_n\\)): Genera una matriz diagonal cuadrada con \\(a_1,a_2,\\ldots,a_n\\) en la diagonal. <\/li>\n<li><strong>ident<\/strong>(<em>N\u00famero<\/em>): Genera la matriz identidad (cuadrada) cuyo tama\u00f1o viene dado por el valor <em>N\u00famero<\/em>; es un caso particular del anterior.<\/li>\n<li><strong>zeromatrix<\/strong>(<em>n<\/em>,<em>m<\/em>): Genera la matriz de <em>n<\/em> filas y <em>m<\/em> columnas en la que todos sus elementos son ceros.<\/li>\n<\/ul>\n<p>Uno de los ejercicios m\u00e1s comunes que realizaremos ser\u00e1 el c\u00e1lculo de rango, determinantes, menores e inversa de una matriz. Primero aprenderemos a realizarlo mediante operaciones elementales, consiguiendo una matriz escalonada o una matriz triangular. No obstante, tenemos los comandos que nos los proporcionan:<\/p>\n<ul>\n<li><strong>rank<\/strong>(\\(M\\)): dada la matriz \\(M\\) nos devuelve su rango.<\/li>\n<li><strong>determinant<\/strong>(\\(M\\)): dada la matriz \\(M\\) nos devuelve su determinante.<\/li>\n<li><strong>mat_trace<\/strong>(\\(M\\)): dada la matriz \\(M\\) nos devuelve su traza.<\/li>\n<li><strong>adjoint<\/strong>(\\(M\\)): dada la matriz \\(M\\) nos devuelve su adjunta.<\/li>\n<li><strong>minor<\/strong>(\\(M,i,j\\)): dada la matriz \\(M\\) nos devuelve el menor (<em>i<\/em>,<em>j<\/em>), esto es, elimina la fila <em>i<\/em> y la columna <em>j<\/em> de la matriz.<\/li>\n<li><strong>invert<\/strong>(\\(M\\)): dada la matriz \\(M\\) nos devuelve su inversa.<\/li>\n<li><strong>invert<\/strong>(\\(M\\)),<strong>detout<\/strong>: dada la matriz \\(M\\) nos devuelve su inversa con el determinante fuera.<\/li>\n<li><strong>ratsimp<\/strong>(<em>expr<\/em>): Simplifica la expresi\u00f3n <em>expr<\/em> y todas sus subexpresiones, incluyendo los argumentos de funciones no racionales. <\/li>\n<\/ul>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Cu\u00e1l es el valor de x para que el rango de la matriz sea 2  \\[\\begin{bmatrix}<br \/>\n5 &#038; -5 &#038; -6\\\\<br \/>\n-5 &#038; 3 &#038; -1 \\\\<br \/>\n0 &#038; x &#038;7<br \/>\n\\end{bmatrix}\\] <\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv71() {\n  var htmlShow71 = document.getElementById(\"html-show71\");\n  if (htmlShow71.style.display === \"none\") {\n    htmlShow71.style.display = \"block\";\n  } else {\n    htmlShow71.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv71()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show71\" style=\"display: none;\">\n<!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/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\">5<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">6<\/span><span class=\"code_operator\">]<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">[<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">\u2212<\/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\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/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_function\">ratsimp<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">determinant<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">A<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\begin{bmatrix}5 &amp; -5 &amp; -6\\\\-5 &amp; 3 &amp; -1\\\\0 &amp; x &amp; 7\\end{bmatrix}\\]<\/p>\n<p>\\[\\operatorname{ }35 x-70\\]<\/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)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">solve<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">%<\/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>\\[\\left[ x=2\\right] \\]<\/p>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> \u00bfQu\u00e9 valores de \\(x\\) hacen que la matriz no sea regular?  \\[\\begin{bmatrix}<br \/>\nx &#038; 1 &#038; -1\\\\<br \/>\n0 &#038; 2 &#038; x \\\\<br \/>\n4 &#038; 0 &#038; -x<br \/>\n\\end{bmatrix}\\] <\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv71e() {\n  var htmlShow71e = document.getElementById(\"html-show71e\");\n  if (htmlShow71e.style.display === \"none\") {\n    htmlShow71e.style.display = \"block\";\n  } else {\n    htmlShow71e.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv71e()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show71e\" style=\"display: none;\">\n<!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/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_variable\">x<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">\u2212<\/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\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/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\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_variable\">x<\/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_function\">determinant<\/span><span class=\"code_operator\">(<\/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>\\[-2 {{x}^{2}}+4 x+8\\]<\/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)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">solve<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">%<\/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>\\[ \\left[ x=1-\\sqrt{5} \\ ,\\ x=\\sqrt{5}+1\\right] \\]<\/p>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong>  \u00bfCu\u00e1l es la ecuaci\u00f3n impl\u00edcita del plano que pasa por los puntos \\(P(1,2,3)\\), \\(Q(-1,0,2)\\) y \\(R(4,-2,0)\\)?  <\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv31() {\n  var htmlShow31 = document.getElementById(\"html-show31\");\n  if (htmlShow31.style.display === \"none\") {\n    htmlShow31.style.display = \"block\";\n  } else {\n    htmlShow31.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv31()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show31\" style=\"display: none;\">\n    <!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"> <span class=\"prompt\">(%i4) <\/span>  <\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"> <span class=\"input\"><span class=\"code_variable\">P<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_number\">1<\/span>,<span class=\"code_number\">2<\/span>,<span class=\"code_number\">3<\/span>]<span class=\"code_endofline\">$<\/span><span class=\"code_variable\">Q<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>,<span class=\"code_number\">0<\/span>,<span class=\"code_number\">2<\/span>]<span class=\"code_endofline\">$<\/span><span class=\"code_variable\">R<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_number\">4<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">2<\/span>,<span class=\"code_number\">0<\/span>]<span class=\"code_endofline\">$<\/span><br \/><span class=\"code_function\">ratsimp<\/span>(<span class=\"code_function\">determinant<\/span>(<span class=\"code_function\">matrix<\/span>([<span class=\"code_variable\">x<\/span>,<span class=\"code_variable\">y<\/span>,<span class=\"code_variable\">z<\/span>]<span class=\"code_operator\">&#8211;<\/span><span class=\"code_variable\">P<\/span>,<span class=\"code_variable\">Q<\/span><span class=\"code_operator\">&#8211;<\/span><span class=\"code_variable\">P<\/span>,<span class=\"code_variable\">R<\/span><span class=\"code_operator\">&#8211;<\/span><span class=\"code_variable\">P<\/span>))<span class=\"code_operator\">=<\/span><span class=\"code_number\">0<\/span>)<span class=\"code_endofline\">;<\/span> <\/span>  <\/td>\n<\/tr>\n<\/table>\n<p> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable>  <mlabeledtr columnalign=\"left\"> <mtd><mtext>(%o4) <\/mtext> <\/mtd> <mtd><mn>14<\/mn><mo>\u2062<\/mo><mi>z<\/mi><mi>\u2212<\/mi><mn>9<\/mn><mo>\u2062<\/mo><mi>y<\/mi><mo>+<\/mo><mn>2<\/mn><mo>\u2062<\/mo><mi>x<\/mi><mi>\u2212<\/mi><mn>26<\/mn><mi>=<\/mi><mn>0<\/mn> <\/mtd>  <\/mlabeledtr><\/mtable> <\/math>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> Justificar si el punto S(2,4,-13) es coplanario con los puntos P(1,-3,-1), Q(2,-2,1) y R(3,2,-4)<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv6q() {\n  var htmlShow6q = document.getElementById(\"html-show6q\");\n  if (htmlShow6q.style.display === \"none\") {\n    htmlShow6q.style.display = \"block\";\n  } else {\n    htmlShow6q.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv6q()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show6q\" style=\"display: none;\">\n<iframe loading=\"lazy\" title=\"\u00c1lgebra Lineal - Puntos Coplanarios. Ej.2 - Jes\u00fas Soto\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/9g6oZ805A5Y?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> \u00bfCu\u00e1l es el valor del producto escalar del vector \\([1,-2,3]\\) por el vector unitario normal de la ecuaci\u00f3n impl\u00edcita del plano que pasa por los puntos \\(P(1,-3,-1)\\), \\(Q(2,-2,1)\\) y \\(R(3,2,-4)\\)?  <\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv72() {\n  var htmlShow72 = document.getElementById(\"html-show72\");\n  if (htmlShow72.style.display === \"none\") {\n    htmlShow72.style.display = \"block\";\n  } else {\n    htmlShow72.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv72()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show72\" style=\"display: none;\">\n<!-- Code cell --> <\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"> <span class=\"prompt\">(%i6) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"> <span class=\"input\"><span class=\"code_variable\">P<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_number\">1<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">3<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>]<span class=\"code_endofline\">;<\/span><span class=\"code_variable\">Q<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_number\">2<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">2<\/span>,<span class=\"code_number\">1<\/span>]<span class=\"code_endofline\">;<\/span><span class=\"code_variable\">R<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_number\">3<\/span>,<span class=\"code_number\">2<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">4<\/span>]<span class=\"code_endofline\">$<\/span><br \/><span class=\"code_variable\">pq<\/span><span class=\"code_operator\">:<\/span><span class=\"code_variable\">Q<\/span><span class=\"code_operator\">&#8211;<\/span><span class=\"code_variable\">P<\/span><span class=\"code_endofline\">$<\/span><br \/><span class=\"code_variable\">pr<\/span><span class=\"code_operator\">:<\/span><span class=\"code_variable\">R<\/span><span class=\"code_operator\">&#8211;<\/span><span class=\"code_variable\">P<\/span><span class=\"code_endofline\">$<\/span><br \/><span class=\"code_function\">rat<\/span>(<span class=\"code_function\">determinant<\/span>(<span class=\"code_function\">matrix<\/span>([<span class=\"code_variable\">x<\/span>,<span class=\"code_variable\">y<\/span>,<span class=\"code_variable\">z<\/span>]<span class=\"code_operator\">&#8211;<\/span><span class=\"code_variable\">P<\/span>,<span class=\"code_variable\">pq<\/span>,<span class=\"code_variable\">pr<\/span>))<span class=\"code_operator\">=<\/span><span class=\"code_number\">0<\/span>)<span class=\"code_endofline\">;<\/span> <\/span><\/td>\n<\/tr>\n<\/table>\n<p> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable><mlabeledtr columnalign=\"left\"> <mtd><mtext>(P)<\/mtext> <\/mtd> <mtd><mo>[<\/mo><mn>1<\/mn><mo>,<\/mo><mi>\u2212<\/mi><mn>3<\/mn><mo>,<\/mo><mi>\u2212<\/mi><mn>1<\/mn><mo>]<\/mo> <\/mtd><\/mlabeledtr><\/mtable> <\/math> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable><mlabeledtr columnalign=\"left\"> <mtd><mtext>(Q)<\/mtext> <\/mtd> <mtd><mo>[<\/mo><mn>2<\/mn><mo>,<\/mo><mi>\u2212<\/mi><mn>2<\/mn><mo>,<\/mo><mn>1<\/mn><mo>]<\/mo> <\/mtd><\/mlabeledtr><\/mtable> <\/math> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable><mlabeledtr columnalign=\"left\"> <mtd><mtext>(%o6)\/R\/ <\/mtext> <\/mtd> <mtd><mn>3<\/mn><mo>\u2062<\/mo><mi>z<\/mi><mo>+<\/mo><mn>7<\/mn><mo>\u2062<\/mo><mi>y<\/mi><mi>\u2212<\/mi><mn>13<\/mn><mo>\u2062<\/mo><mi>x<\/mi><mo>+<\/mo><mn>37<\/mn><mi>=<\/mi><mn>0<\/mn> <\/mtd><\/mlabeledtr><\/mtable> <\/math> <!-- Code cell --> <\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"> <span class=\"prompt\">(%i8) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"> <span class=\"input\"><span class=\"code_variable\">vn<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">13<\/span>,<span class=\"code_number\">7<\/span>,<span class=\"code_number\">3<\/span>]<span class=\"code_endofline\">$<\/span><br \/>(<span class=\"code_variable\">vn<\/span><span class=\"code_number\">.[<\/span><span class=\"code_number\">1<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">2<\/span>,<span class=\"code_number\">3<\/span>])<span class=\"code_operator\">\/<\/span><span class=\"code_function\">sqrt<\/span>(<span class=\"code_variable\">vn<\/span>.<span class=\"code_variable\">vn<\/span>),<span class=\"code_variable\">numer<\/span><span class=\"code_endofline\">;<\/span> <\/span><\/td>\n<\/tr>\n<\/table>\n<p> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable><mlabeledtr columnalign=\"left\"> <mtd><mtext>(%o8) <\/mtext> <\/mtd> <mtd><mi>\u2212<\/mi><mn>1.19470196087995<\/mn> <\/mtd><\/mlabeledtr><\/mtable> <\/math>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> \u00bfCu\u00e1l es la norma del vector perpendicular a los vectores \\(\\vec{v}:[1,-2,3]\\) y \\(\\vec{u}:[3,1,-1]\\)? <\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv3a() {\n  var htmlShow3a = document.getElementById(\"html-show3a\");\n  if (htmlShow3a.style.display === \"none\") {\n    htmlShow3a.style.display = \"block\";\n  } else {\n    htmlShow3a.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv3a()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show3a\" style=\"display: none;\">\n <!-- Code cell -->  <\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"> <span class=\"prompt\">(%i4) <\/span>  <\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"> <span class=\"input\"><span class=\"code_variable\">v<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_number\">1<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">2<\/span>,<span class=\"code_number\">3<\/span>]<span class=\"code_endofline\">$<\/span><span class=\"code_variable\">u<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_number\">3<\/span>,<span class=\"code_number\">1<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>]<span class=\"code_endofline\">$<\/span><br \/><span class=\"code_variable\">A<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">matrix<\/span>([<span class=\"code_number\">1<\/span>,<span class=\"code_number\">1<\/span>,<span class=\"code_number\">1<\/span>],<span class=\"code_variable\">v<\/span>,<span class=\"code_variable\">u<\/span>)<span class=\"code_endofline\">$<\/span><br \/><span class=\"code_variable\">vxu<\/span><span class=\"code_operator\">:<\/span>[<span class=\"code_function\">determinant<\/span>(<span class=\"code_function\">minor<\/span>(<span class=\"code_variable\">A<\/span>,<span class=\"code_number\">1<\/span>,<span class=\"code_number\">1<\/span>)),<br \/>    <span class=\"code_operator\">&#8211;<\/span><span class=\"code_function\">determinant<\/span>(<span class=\"code_function\">minor<\/span>(<span class=\"code_variable\">A<\/span>,<span class=\"code_number\">1<\/span>,<span class=\"code_number\">2<\/span>)),<br \/>    <span class=\"code_function\">determinant<\/span>(<span class=\"code_function\">minor<\/span>(<span class=\"code_variable\">A<\/span>,<span class=\"code_number\">1<\/span>,<span class=\"code_number\">3<\/span>))]<span class=\"code_endofline\">;<\/span> <\/span>  <\/td>\n<\/tr>\n<\/table>\n<p> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable>  <mlabeledtr columnalign=\"center\"> <mtd><mtext>(vxu)<\/mtext> <\/mtd> <mtd><mo>[<\/mo><mi>\u2212<\/mi><mn>1<\/mn><mo>,<\/mo><mn>10<\/mn><mo>,<\/mo><mn>7<\/mn><mo>]<\/mo> <\/mtd>  <\/mlabeledtr><\/mtable> <\/math> <!-- Code cell --> <\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"> <span class=\"prompt\">(%i5) <\/span>  <\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"> <span class=\"input\"><span class=\"code_function\">sqrt<\/span>(<span class=\"code_variable\">vxu<\/span>.<span class=\"code_variable\">vxu<\/span>),<span class=\"code_variable\">numer<\/span><span class=\"code_endofline\">;<\/span> <\/span>  <\/td>\n<\/tr>\n<\/table>\n<p> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable>  <mlabeledtr columnalign=\"center\"> <mtd><mtext>(%o5) <\/mtext> <\/mtd> <mtd><mn>12.24744871391589<\/mn> <\/mtd>  <\/mlabeledtr><\/mtable> <\/math>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> \u00bfCu\u00e1l es la traza de la inversa de la matriz \\(A\\)=[[3,0,-1,1], [1,1,2,-1],[0,1,-1,0], [1,2,0,-1]]? <\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv3b() {\n  var htmlShow3b = document.getElementById(\"html-show3b\");\n  if (htmlShow3b.style.display === \"none\") {\n    htmlShow3b.style.display = \"block\";\n  } else {\n    htmlShow3b.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv3b()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show3b\" style=\"display: none;\">\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"> <span class=\"prompt\">(%i3) <\/span>  <\/td>\n<td> <span class=\"input\"><span class=\"code_variable\">A<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">matrix<\/span>([<span class=\"code_number\">3<\/span>,<span class=\"code_number\">0<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>,<span class=\"code_number\">1<\/span>],[<span class=\"code_number\">1<\/span>,<span class=\"code_number\">1<\/span>,<span class=\"code_number\">2<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>],<br \/>    [<span class=\"code_number\">0<\/span>,<span class=\"code_number\">1<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>,<span class=\"code_number\">0<\/span>],[<span class=\"code_number\">1<\/span>,<span class=\"code_number\">2<\/span>,<span class=\"code_number\">0<\/span>,<span class=\"code_number\">&#8211;<\/span><span class=\"code_number\">1<\/span>])<span class=\"code_endofline\">$<\/span><br \/><span class=\"code_variable\">invA<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">invert<\/span>(<span class=\"code_variable\">A<\/span>)<span class=\"code_endofline\">;<\/span><br \/><span class=\"code_function\">mat_trace<\/span>(<span class=\"code_variable\">A<\/span>)<span class=\"code_endofline\">;<\/span> <\/span>  <\/td>\n<\/tr>\n<\/table>\n<p> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable>  <mlabeledtr columnalign=\"center\"> <mtd><mtext>(invA)<\/mtext> <\/mtd> <mtd><mrow>  <mo>[<\/mo>  <mrow> <mtable><mtr>  <mtd> <mfrac><mn>1<\/mn><mn>4<\/mn> <\/mfrac>  <\/mtd>  <mtd> <mrow><mi>\u2212<\/mi><mfrac>  <mn>1<\/mn>  <mn>4<\/mn><\/mfrac> <\/mrow>  <\/mtd>  <mtd> <mrow><mi>\u2212<\/mi><mfrac>  <mn>3<\/mn>  <mn>4<\/mn><\/mfrac> <\/mrow>  <\/mtd>  <mtd> <mfrac><mn>1<\/mn><mn>2<\/mn> <\/mfrac>  <\/mtd><\/mtr><mtr>  <mtd> <mn>0<\/mn>  <\/mtd>  <mtd> <mn>1<\/mn>  <\/mtd>  <mtd> <mn>2<\/mn>  <\/mtd>  <mtd> <mrow><mi>\u2212<\/mi><mn>1<\/mn> <\/mrow>  <\/mtd><\/mtr><mtr>  <mtd> <mn>0<\/mn>  <\/mtd>  <mtd> <mn>1<\/mn>  <\/mtd>  <mtd> <mn>1<\/mn>  <\/mtd>  <mtd> <mrow><mi>\u2212<\/mi><mn>1<\/mn> <\/mrow>  <\/mtd><\/mtr><mtr>  <mtd> <mfrac><mn>1<\/mn><mn>4<\/mn> <\/mfrac>  <\/mtd>  <mtd> <mfrac><mn>7<\/mn><mn>4<\/mn> <\/mfrac>  <\/mtd>  <mtd> <mfrac><mn>13<\/mn><mn>4<\/mn> <\/mfrac>  <\/mtd>  <mtd> <mrow><mi>\u2212<\/mi><mfrac>  <mn>5<\/mn>  <mn>2<\/mn><\/mfrac> <\/mrow>  <\/mtd><\/mtr> <\/mtable>  <\/mrow>  <mo>]<\/mo><\/mrow> <\/mtd>  <\/mlabeledtr>  <mlabeledtr columnalign=\"center\"> <mtd><mtext\/> <\/mtd> <mtd><mo>0 errores, 0 advertencias<\/mo> <\/mtd>  <\/mlabeledtr><\/mtable> <\/math> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable>  <mlabeledtr columnalign=\"center\"> <mtd><mtext>(%o3) <\/mtext> <\/mtd> <mtd><mn>2<\/mn> <\/mtd>  <\/mlabeledtr><\/mtable> <\/math>\n<\/div>\n<hr \/>\n<h3>Bibliograf\u00eda<\/h3>\n<ul>\n<li>Arriaza G\u00f3mez A. J., del \u00c1guila Garrido L., Rambla Barreno F., Redondo Neble M. V., Rodr\u00edguez Galv\u00e1n J. R., Viglialoro G. Manual de pr\u00e1cticas de Matem\u00e1ticas con M\u00e1xima. C\u00e1diz: Editorial UCA; 2015.<\/li>\n<\/ul>\n<hr \/>\n<table id=\"yzpi\" border=\"0\" width=\"100%\" cellspacing=\"0\" cellpadding=\"3\" bgcolor=\"#999999\">\n<tbody>\n<tr>\n<td width=\"100%\"><strong>Ejercicio:<\/strong> Sea la matriz [[1,2,-3],[-2,0,4],[0,4,-2],[-2,-4,\\(a\\)]], \u00bfcu\u00e1l es el valor de \\(a\\) para que el rango de la matriz sea par? <\/td>\n<\/tr>\n<tr>\n<td>\n<div id=\"menu-a\">\n<ul>\n<li>3<\/li>\n<li>6<\/li>\n<li>9<\/li>\n<\/ul>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><script>\nfunction showHtmlDiv() {\n  var htmlShow = document.getElementById(\"html-show\");\n  if (htmlShow.style.display === \"none\") {\n    htmlShow.style.display = \"block\";\n  } else {\n    htmlShow.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show\" style=\"display: none;\">\n<p><strong>B.)<\/strong><\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/uploads.jesussoto.es\/maxima\/ejrALGmatriz02.html\" width=\"650\" height=\"300\" allow=\"fullscreen\"><\/iframe>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Hoy nos iniciamos en un sistema para la manipulaci\u00f3n de expresiones simb\u00f3licas y num\u00e9ricas, Maxima. Un herramienta inform\u00e1tica que nos ayudar\u00e1 a resolver problemas de la asignatura de forma sencilla y aplicada&#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":[5],"class_list":["post-69","post","type-post","status-publish","format-standard","hentry","category-mathbio","tag-practicas-mathbio"],"_links":{"self":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/69","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=69"}],"version-history":[{"count":4,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/69\/revisions"}],"predecessor-version":[{"id":229,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/69\/revisions\/229"}],"wp:attachment":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=69"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=69"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=69"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}