{"id":852,"date":"2021-11-27T22:47:37","date_gmt":"2021-11-27T22:47:37","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=852"},"modified":"2022-02-08T20:49:06","modified_gmt":"2022-02-08T20:49:06","slug":"clase-digital-13-espacios-vectoriales","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-13-espacios-vectoriales\/","title":{"rendered":"Clase digital 13: Espacios vectoriales"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"has-background-dim-40 wp-block-cover__gradient-background has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-853\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/hatkch_piqm.jpg\" style=\"object-position:45% 27%\" data-object-fit=\"cover\" data-object-position=\"45% 27%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1200\" class=\"wp-block-cover__image-background wp-image-853\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/hatkch_piqm.jpg\" style=\"object-position:45% 27%\" data-object-fit=\"cover\" data-object-position=\"45% 27%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/hatkch_piqm.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/hatkch_piqm-300x225.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/hatkch_piqm-1024x768.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/hatkch_piqm-768x576.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/hatkch_piqm-1536x1152.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\">Espacios vectoriales<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Hola!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es un gusto saber que contin\u00faas en este camino formativo, en esta ocasi\u00f3n nos encontramos en la clase 13 denominada Espacios vectoriales del curso <strong>\u00c1lgebra lineal.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Antes que nada, espero que est\u00e9s teniendo un excelente d\u00eda y que te encuentres bastante bien. Del mismo modo, te invito a participar y completar las consignas correspondientes para esta sesi\u00f3n.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Los espacios vectoriales son conjuntos de <strong>vectores<\/strong> que permiten dos operaciones binarias:<ul><li>Multiplicaci\u00f3n por escalar.<\/li><li>Suma<\/li><\/ul><\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Veremos que no todas las ecuaciones cumplen con estas condiciones por lo que no son espacios vectoriales. A su vez el entendimiento de este tema nos permitir\u00e1 abordar las siguientes sesiones sobre combinaciones lineales y conjuntos generadores.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Esperamos que la sesi\u00f3n sea de tu agrado y te invito a proseguir con tu mismo \u00e1nimo.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema <\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>Los <strong>espacios vectoriales <\/strong>son conjuntos de <strong>vectores<\/strong> que permiten dos operaciones binarias:<ul><li>Multiplicaci\u00f3n por escalar.<\/li><li>Suma<\/li><\/ul><\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo 1:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Poseemos la ecuaci\u00f3n:<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>x &#8211; y = 0<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.48.44.png\" alt=\"\" class=\"wp-image-854\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"384\" height=\"434\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.48.44.png\" alt=\"\" class=\"wp-image-854\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.48.44.png 384w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.48.44-265x300.png 265w\" sizes=\"auto, (max-width: 384px) 100vw, 384px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Si otorgamos el valor de:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>x = 5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Entonces:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">&nbsp; <strong>y = 5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>O bien, de forma matricial<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.49.39.png\" alt=\"\" class=\"wp-image-855\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"332\" height=\"497\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.49.39.png\" alt=\"\" class=\"wp-image-855\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.49.39.png 332w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.49.39-200x300.png 200w\" sizes=\"auto, (max-width: 332px) 100vw, 332px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>NOTA: Observa que el par de n\u00fameros se encuentra en la recta.&nbsp;<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si al par x = 5, y = 5 <em>(o mejor dicho <\/em><strong><em>vector<\/em><\/strong><em>), <\/em>lo multiplicamos por cualquier escalar, por ejemplo -1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Obtenemos un segundo vector:&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>X = -5<\/strong><br><strong>Y = -5<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.50.20.png\" alt=\"\" class=\"wp-image-856\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"335\" height=\"480\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.50.20.png\" alt=\"\" class=\"wp-image-856\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.50.20.png 335w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.50.20-209x300.png 209w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>NOTA: Observa que el vector multiplicado por un escalar sigue estando en la recta.&nbsp;&nbsp;<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se ve entonces que si a un par de respuestas correctas (x, y), se le multiplica cualquier escalar (c), esto dar\u00e1 otro conjunto de respuestas correctas:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.50.48.png\" alt=\"\" class=\"wp-image-857\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"412\" height=\"131\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.50.48.png\" alt=\"\" class=\"wp-image-857\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.50.48.png 412w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.50.48-300x95.png 300w\" sizes=\"auto, (max-width: 412px) 100vw, 412px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.51.15.png\" alt=\"\" class=\"wp-image-858\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"334\" height=\"298\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.51.15.png\" alt=\"\" class=\"wp-image-858\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.51.15.png 334w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.51.15-300x268.png 300w\" sizes=\"auto, (max-width: 334px) 100vw, 334px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Observemos que si sumamos dos vectores de respuestas correctas nos dar\u00e1 como resultado otra respuesta correcta.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>EJEMPLO:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sabemos que el par x=5 y=5 resuelve la ecuaci\u00f3n. Lo llamaremos vector 1 (V1).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Igual que X=-5, y = -5. Ser\u00e1 vector 2 (V2).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.51.57.png\" alt=\"\" class=\"wp-image-859\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"672\" height=\"344\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.51.57.png\" alt=\"\" class=\"wp-image-859\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.51.57.png 672w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.51.57-300x154.png 300w\" sizes=\"auto, (max-width: 672px) 100vw, 672px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se concluye que: <strong>x &#8211; y = 0<\/strong> Es un <strong>ESPACIO VECTORIAL<\/strong>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.52.35.png\" alt=\"\" class=\"wp-image-860\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"304\" height=\"452\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.52.35.png\" alt=\"\" class=\"wp-image-860\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.52.35.png 304w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.52.35-202x300.png 202w\" sizes=\"auto, (max-width: 304px) 100vw, 304px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>EJEMPLO 2<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Poseemos la ecuaci\u00f3n: <strong>x &#8211; y = 5<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.53.52.png\" alt=\"\" class=\"wp-image-861\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"346\" height=\"490\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.53.52.png\" alt=\"\" class=\"wp-image-861\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.53.52.png 346w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.53.52-212x300.png 212w\" sizes=\"auto, (max-width: 346px) 100vw, 346px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Si otorgamos el valor de:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>x = 0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Entonces:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>y = -5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>O bien, de forma matricial<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.54.36.png\" alt=\"\" class=\"wp-image-862\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"319\" height=\"271\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.54.36.png\" alt=\"\" class=\"wp-image-862\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.54.36.png 319w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.54.36-300x255.png 300w\" sizes=\"auto, (max-width: 319px) 100vw, 319px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.55.02.png\" alt=\"\" class=\"wp-image-863\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"296\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.55.02.png\" alt=\"\" class=\"wp-image-863\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.55.02.png 343w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.55.02-300x259.png 300w\" sizes=\"auto, (max-width: 343px) 100vw, 343px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Si al vector x = 0, y = 5<em>, <\/em>lo multiplicamos por cualquier escalar, por ejemplo -1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Obtenemos un segundo vector:&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>X = 0<\/strong><br><strong>Y = 5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>NOTA: Observa que el vector multiplicado por un escalar <\/em><strong><em>est\u00e1 fuera de la recta<\/em><\/strong><em>.<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.55.49.png\" alt=\"\" class=\"wp-image-864\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"402\" height=\"338\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.55.49.png\" alt=\"\" class=\"wp-image-864\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.55.49.png 402w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.55.49-300x252.png 300w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Si sumamos dos vectores de respuestas correctas:<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">V1;<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>X = 0<\/strong><br><strong>Y = -5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">V2;&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>X = 5<\/strong><br><strong>Y = 0<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.56.37.png\" alt=\"\" class=\"wp-image-865\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"627\" height=\"430\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.56.37.png\" alt=\"\" class=\"wp-image-865\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.56.37.png 627w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.56.37-300x206.png 300w\" sizes=\"auto, (max-width: 627px) 100vw, 627px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se concluye que la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>x &#8211; y = 5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>NO ES ESPACIO VECTORIAL<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.57.15.png\" alt=\"\" class=\"wp-image-866\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"332\" height=\"468\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.57.15.png\" alt=\"\" class=\"wp-image-866\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.57.15.png 332w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.57.15-213x300.png 213w\" sizes=\"auto, (max-width: 332px) 100vw, 332px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><em>NOTAS<\/em>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recuerda que si realizamos un producto escalar de:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.57.48.png\" alt=\"\" class=\"wp-image-867\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"232\" height=\"105\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.57.48.png\" alt=\"\" class=\"wp-image-867\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Obtenemos:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">(1) (x) + (-1) (y) = 0<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.58.16.png\" alt=\"\" class=\"wp-image-868\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"129\" height=\"43\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-09-a-las-12.58.16.png\" alt=\"\" class=\"wp-image-868\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Tip: TODAS las <strong>ecuaciones de rectas que pasen por el origen <\/strong><em>(coordenada 0,0) <\/em>son espacios vectoriales.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En resumen:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Se puede decir que los <strong>espacios vectoriales <\/strong>son CUALQUIER REPRESENTACI\u00d3N MATEM\u00c1TICA donde una respuesta correcta <strong>multiplicada por un escalar<\/strong>, dar\u00e1 como resultado otra respuesta correcta.&nbsp;<\/li><li>Y al <strong>sumar<\/strong> dos respuestas correctas diferentes de un espacio vectorial nos da como resultado otra respuesta correcta.&nbsp;<\/li><li>Del mismo modo, si multiplicamos un vector de cualquier espacio vectorial por un n\u00famero escalar, entonces el resultado tambi\u00e9n estar\u00e1 dentro del mismo espacio vectorial.&nbsp;<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Hemos llegado al final de la clase \u00a1Te felicito por tu logro! Para completar la sesi\u00f3n te pido que realices la tarea asignada. Sigue avanzando en tu curso, falta poco para que logres completarlo. Te espero en la siguiente clase, hasta luego.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n <\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>Grossman, S. I. (2004). Algebra Lineal y sus Aplicaciones. (5<sup>a<\/sup> ed.). M\u00e9xico: McGraw-Hill.<\/li><li>Anton, H. (2011). Introducci\u00f3n al Algebra Lineal. (5<sup>a<\/sup> ed.). M\u00e9xico: Limusa Wiley.<\/li><li>Campbell, H. G. (1980). Linear Algebra with Applications. Atlanta: Prentice-Hall.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Es un gusto saber que contin\u00faas en este camino formativo, en esta ocasi\u00f3n nos encontramos en la clase 13 denominada Espacios vectoriales del curso \u00c1lgebra lineal. Antes que nada, espero que est\u00e9s teniendo un excelente d\u00eda y que te encuentres bastante bien. Del mismo modo, te invito a participar y completar las consignas &#8230; <a title=\"Clase digital 13: Espacios vectoriales\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-13-espacios-vectoriales\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 13: Espacios vectoriales\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[10,11],"tags":[41,61,62],"class_list":["post-852","post","type-post","status-publish","format-standard","hentry","category-ingenieria-civil","category-uda-algebra-lineal","tag-clase-digital","tag-jorge-arturo-gutierrez-camarena","tag-neli04035"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/852","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=852"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/852\/revisions"}],"predecessor-version":[{"id":7313,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/852\/revisions\/7313"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=852"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=852"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=852"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}