{"id":14226,"date":"2018-06-15T19:27:44","date_gmt":"2018-06-15T19:27:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/solutions-35\/"},"modified":"2022-01-09T20:12:59","modified_gmt":"2022-01-09T20:12:59","slug":"solutions-cramers-rule","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/solutions-cramers-rule\/","title":{"raw":"Solutions:  Solving Systems with Cramer's Rule","rendered":"Solutions:  Solving Systems with Cramer&#8217;s Rule"},"content":{"raw":"<h2>Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0A determinant is the sum and products of the entries in the matrix, so you can always evaluate that product\u2014even if it does end up being 0.\r\n\r\n3.\u00a0The inverse does not exist.\r\n\r\n5.\u00a0[latex]-2[\/latex]\r\n\r\n7.\u00a0[latex]7[\/latex]\r\n\r\n9.\u00a0[latex]-4[\/latex]\r\n\r\n11.\u00a0[latex]0[\/latex]\r\n\r\n13.\u00a0[latex]-7,990.7[\/latex]\r\n\r\n15.\u00a0[latex]3[\/latex]\r\n\r\n17.\u00a0[latex]-1[\/latex]\r\n\r\n19.\u00a0[latex]224[\/latex]\r\n\r\n21.\u00a0[latex]15[\/latex]\r\n\r\n23.\u00a0[latex]-17.03[\/latex]\r\n\r\n25.\u00a0[latex]\\left(1,1\\right)[\/latex]\r\n\r\n27.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{3}\\right)[\/latex]\r\n\r\n29.\u00a0[latex]\\left(2,5\\right)[\/latex]\r\n\r\n31.\u00a0[latex]\\left(-1,-\\frac{1}{3}\\right)[\/latex]\r\n\r\n33.\u00a0[latex]\\left(15,12\\right)[\/latex]\r\n\r\n35.\u00a0[latex]\\left(1,3,2\\right)[\/latex]\r\n\r\n37.\u00a0[latex]\\left(-1,0,3\\right)[\/latex]\r\n\r\n39.\u00a0[latex]\\left(\\frac{1}{2},1,2\\right)[\/latex]\r\n\r\n41.\u00a0[latex]\\left(2,1,4\\right)[\/latex]\r\n\r\n43.\u00a0Infinite solutions\r\n\r\n45.\u00a0[latex]24[\/latex]\r\n\r\n47.\u00a0[latex]1[\/latex]","rendered":"<h2>Solutions to Odd-Numbered Exercises<\/h2>\n<p>1.\u00a0A determinant is the sum and products of the entries in the matrix, so you can always evaluate that product\u2014even if it does end up being 0.<\/p>\n<p>3.\u00a0The inverse does not exist.<\/p>\n<p>5.\u00a0[latex]-2[\/latex]<\/p>\n<p>7.\u00a0[latex]7[\/latex]<\/p>\n<p>9.\u00a0[latex]-4[\/latex]<\/p>\n<p>11.\u00a0[latex]0[\/latex]<\/p>\n<p>13.\u00a0[latex]-7,990.7[\/latex]<\/p>\n<p>15.\u00a0[latex]3[\/latex]<\/p>\n<p>17.\u00a0[latex]-1[\/latex]<\/p>\n<p>19.\u00a0[latex]224[\/latex]<\/p>\n<p>21.\u00a0[latex]15[\/latex]<\/p>\n<p>23.\u00a0[latex]-17.03[\/latex]<\/p>\n<p>25.\u00a0[latex]\\left(1,1\\right)[\/latex]<\/p>\n<p>27.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{3}\\right)[\/latex]<\/p>\n<p>29.\u00a0[latex]\\left(2,5\\right)[\/latex]<\/p>\n<p>31.\u00a0[latex]\\left(-1,-\\frac{1}{3}\\right)[\/latex]<\/p>\n<p>33.\u00a0[latex]\\left(15,12\\right)[\/latex]<\/p>\n<p>35.\u00a0[latex]\\left(1,3,2\\right)[\/latex]<\/p>\n<p>37.\u00a0[latex]\\left(-1,0,3\\right)[\/latex]<\/p>\n<p>39.\u00a0[latex]\\left(\\frac{1}{2},1,2\\right)[\/latex]<\/p>\n<p>41.\u00a0[latex]\\left(2,1,4\\right)[\/latex]<\/p>\n<p>43.\u00a0Infinite solutions<\/p>\n<p>45.\u00a0[latex]24[\/latex]<\/p>\n<p>47.\u00a0[latex]1[\/latex]<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-14226\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: OpenStax College. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":23485,"menu_order":26,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Precalculus\",\"author\":\"OpenStax College\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-14226","chapter","type-chapter","status-publish","hentry"],"part":13184,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/14226","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/23485"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/14226\/revisions"}],"predecessor-version":[{"id":16690,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/14226\/revisions\/16690"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/13184"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/14226\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=14226"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=14226"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=14226"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=14226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}