{"id":901,"date":"2021-10-05T09:48:58","date_gmt":"2021-10-05T07:48:58","guid":{"rendered":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=901"},"modified":"2021-10-05T09:48:58","modified_gmt":"2021-10-05T07:48:58","slug":"suma-resta-y-productos-numericos-con-matrices","status":"publish","type":"post","link":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=901","title":{"rendered":"Suma, resta y productos num\u00e9ricos con matrices"},"content":{"rendered":"<style type=\"text\/css\">\nboton {\n border: none;\n background: rgba(0,0,0,0);\n color: #3a7999;\n box-shadow: inset 0 0 0 3px #3a7999;\n padding: 10px;\n font-size: 125%;\n border-radius: 5px;\n position: relative;\n box-sizing: border-box;\n}\n<\/style>\n<p><script type=\"text\/javascript\">function SINO(cual) {\n   var elElemento=document.getElementById(cual);\n   if(elElemento.style.display == 'block') {\n      elElemento.style.display = 'none';\n   } else {\n      elElemento.style.display = 'block';\n   }\n}\n<\/script><\/p>\n<p>Hola de nuevo. Hoy dedico esta entrada a las operaciones m\u00e1s sencillas con las matrices: la suma, la resta y el producto por n\u00fameros.<\/p>\n<p>Es muy f\u00e1cil sumar (o restar) dos matrices de iguales dimensiones: sumamos (o restamos) los elementos que ocupan las correspondientes posiciones en ambas. Y para multiplicar una matriz por un n\u00famero simplemente multiplicamos por \u00e9l todas los elementos que componen la matriz.<\/p>\n<p>Aunque es algo simple, os propongo trabajar las ideas y los ejemplos conmigo a trav\u00e9s del siguiente v\u00eddeo:<\/p>\n<div style=\"text-align: center;\">\n<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/ZCwiZWfvSwk\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<\/div>\n<p>Os propongo una breve:<\/p>\n<form name=\"ejercicio\">\n<fieldset style=\"border: 1px solid #8A0808; padding: 10px;\">\n<div class=\"pregunta\">\n<div style=\"text-align: center;\">CUESTI\u00d3N<\/div>\n<p>Dadas las matrices<br \/>\n\\[A = \\left( \\begin{array}{rcr}1&amp;2&amp;-3\\\\0&amp;1&amp;3\\\\ \\end{array} \\right)<br \/>\n\\quad , \\quad<br \/>\nB = \\left(\\begin{array}{rrr}1&amp;-1&amp;2\\\\1&amp;0&amp;8\\\\\\end{array}\\right)\\]<br \/>\nlos elementos \\(c_{12}\\) y \\(c_{13}\\) de \\(C=2A-3B^{\\,t}\\) son, respectivamente:<\/p>\n<table width=\"100%\" cellpadding=\"4\" cellspacing=\"0\">\n<tr>\n<td width=\"90%\" style=\"border: none;\">\n<p align=\"left\"><input name=\"p1\" onclick=\"document.ejercicio.feedback1.value=' &#10060; Incorrecto '\" type=\"radio\" \/> 1 y 0.<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"10%\" style=\"border: none;\">\n<p align=\"center\"><boton><a href=\"javascript:void(0);\" onclick=\"SINO('suger1')\" style=\"text-decoration: none;\" title=\"Ver sugerencia\">&#10067;<\/a><\/boton><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90%\" style=\"border: none;\">\n<p align=\"left\"><input name=\"p1\" onclick=\"document.ejercicio.feedback1.value=' &#9989; Correcto '\" type=\"radio\" \/> 7 y &minus;12.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90%\" style=\"border: none;\">\n<p align=\"left\"><input name=\"p1\" onclick=\"document.ejercicio.feedback1.value=' &#10060; Incorrecto '\" type=\"radio\" \/> 1 y &minus;12.<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"10%\" style=\"border: none;\">\n<p align=\"center\"><boton><a href=\"javascript:void(0);\" onclick=\"SINO('solu1')\" style=\"text-decoration: none;\" title=\"Ver soluci\u00f3n\"> &#9997; <\/a><\/boton><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90%\" style=\"border: none;\">\n<p align=\"left\"><input name=\"p1\" onclick=\"document.ejercicio.feedback1.value=' &#10060; Incorrecto '\" type=\"radio\" \/> 7 y 0.<\/p>\n<\/td>\n<\/tr>\n<\/table>\n<div style=\"text-align: center;\"><input name=\"feedback1\" size=\"10\" \/><\/div>\n<p>\n<\/div>\n<div id=\"suger1\" style=\"display: none;\">\n<hr \/>\n<p>Sugerencia:<\/p>\n<p>Calculemos la matriz resultante teniendo en cuenta que, en primer lugar trasponemos \\(B\\), en segundo multiplicamos cada elemento de las matrices por el n\u00famero coeficiente y en tercer lugar restaremos los elementos correspondientes.<\/p>\n<\/div>\n<div id=\"solu1\" style=\"display: none;\">\n<hr \/>\n<p>Soluci\u00f3n:<\/p>\n<p>Calculamos la matriz:<br \/>\n\\[2A-3B^{\\,t}= \\left( \\begin{array}{rcr}2&amp;4&amp;-6\\\\0&amp;2&amp;6\\\\ \\end{array} \\right)-\\left( \\begin{array}{rrc}3&amp;-3&amp;6\\\\3&amp;0&amp;24\\\\ \\end{array} \\right)\\]<br \/>\nLuego<br \/>\n\\[C=\\left( \\begin{array}{rcr}-1&amp;7&amp;-12\\\\3&amp;2&amp;-18\\\\ \\end{array} \\right) \\rightarrow c_{12}=7 \\text{ y }c_{13}=-12 \\]\n<\/p><\/div>\n<\/fieldset>\n<p>\n<\/form>\n<p>Supongo que no habr\u00e1s tenido en estos menesteres dificultades. Gracias y hasta pronto.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hola de nuevo. Hoy dedico esta entrada a las operaciones m\u00e1s sencillas con las matrices: la suma, la resta y el producto [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31],"tags":[65,64,50],"class_list":["post-901","post","type-post","status-publish","format-standard","hentry","category-matematicas-aplicadas-ii","tag-algebra","tag-matrices-y-determinantes","tag-video"],"_links":{"self":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/901","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=901"}],"version-history":[{"count":1,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/901\/revisions"}],"predecessor-version":[{"id":902,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/901\/revisions\/902"}],"wp:attachment":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=901"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=901"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=901"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}