{"id":52,"date":"2013-09-25T20:12:36","date_gmt":"2013-09-25T20:12:36","guid":{"rendered":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/?p=52"},"modified":"2013-09-25T20:12:36","modified_gmt":"2013-09-25T20:12:36","slug":"homework-5","status":"publish","type":"post","link":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/2013\/09\/25\/homework-5\/","title":{"rendered":"Homework 5"},"content":{"rendered":"<p>Due Wednesday, October 2, in class<\/p>\n<p>Section 2.2 problems 1, 4, 14, 15, 16<br \/>\nSection 2.3 problems 1, 3, 10, 16<\/p>\n<p>Then<\/p>\n<p>A. Let \\(V,W\\) be vector spaces over \\(F\\) with ordered bases \\(\\beta = \\{v_1,\\ldots, v_n\\}\\) and \\(\\gamma = \\{ w_1,\\ldots, w_m\\}\\), respectively. Show that the function \\(G:\\ \\mathcal{L}(V,W) \\to M_{m\\times n}(F)\\) given by \\(G(T) = [T]_\\beta^\\gamma\\) is a linear transformation.  (Side note: \\(G\\) is an element of \\(\\mathcal{L}(\\mathcal{L}(V,W), M_{m\\times n}(F)).\\)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Due Wednesday, October 2, in class Section 2.2 problems 1, 4, 14, 15, 16 Section 2.3 problems 1, 3, 10, 16 Then A. Let \\(V,W\\) be vector spaces over \\(F\\) with ordered bases \\(\\beta = \\{v_1,\\ldots, v_n\\}\\) and \\(\\gamma = \\{ w_1,\\ldots, w_m\\}\\), respectively. Show that the function \\(G:\\ \\mathcal{L}(V,W) \\to M_{m\\times n}(F)\\) given by [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/posts\/52"}],"collection":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/comments?post=52"}],"version-history":[{"count":14,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/posts\/52\/revisions"}],"predecessor-version":[{"id":66,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/posts\/52\/revisions\/66"}],"wp:attachment":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/media?parent=52"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/categories?post=52"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2013mat531\/wp-json\/wp\/v2\/tags?post=52"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}