{"id":803,"date":"2014-08-25T19:59:34","date_gmt":"2014-08-25T23:59:34","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/fgarvan\/?page_id=803"},"modified":"2026-03-19T08:11:14","modified_gmt":"2026-03-19T12:11:14","slug":"ch1","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/fgarvan\/teaching\/linalg\/sughw\/ch1\/","title":{"rendered":"Chapter 1 &#8211; Vector Spaces"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<ul class=\"wp-block-list\"><li>1.2 Vector Spaces (pp.13-15):<br>\n1, 2, 3, 4, 7, 8, 9, 10, 11, 13, 14, 15, 17<\/li>\n<li>1.3 Subspaces (pp.19-23):<br>\n1, 2, 3, 4, 5, 8, 10, 11, 13, 17, 20, 23, 24, 26, 30<\/li>\n<li>1.4 Linear Combinations and Systems of lInear Equations (pp.33-34):<br>\n1, 2ace, 3ace, 4ae, 5ace, 6, 8, 9, 10, 11, 12, 13, 15<\/li>\n<li>1.5 Linear Dependence and Linear Independence (pp.40-42):<br>\n1, 2(a)-(f), 3, 7, 8, 9, 10, 11, 12, 13, 14, 19, 20<br>\nNOTE:<br>\n* Problem 14 was done in class.<br>\n* In a field of characteristic 2 we have 1+1=0.<br>\n* Z<sub>2<\/sub>={0,1} is the field of two elements:<!--PARAGRAPH_SEPARATOR--><pre>   + | 0 1     * | 0 1\r\n   -------     -------\r\n   0 | 0 1     0 | 0 0\r\n   1 | 1 0     1 | 0 1\r\n<\/pre>\n<\/li>\n<li>1.6 Bases and Dimension (pp.53-55):<br>\n1, 2(b), 3(c), 4, 5, 7, 11, 12, 14, 19,22,26.<\/li>\n<\/ul>\n\n\n\n<p>Last update made Fri Sep 12 16:07:28 EDT 2014.<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":140,"featured_media":0,"parent":801,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-803","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages\/803","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/users\/140"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/comments?post=803"}],"version-history":[{"count":9,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages\/803\/revisions"}],"predecessor-version":[{"id":3490,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages\/803\/revisions\/3490"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/pages\/801"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/fgarvan\/wp-json\/wp\/v2\/media?parent=803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}