{"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":"2021-06-03T21:16:10","modified_gmt":"2021-06-03T21:16:10","slug":"solutions-35","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/solutions-35\/","title":{"raw":"Solutions 2.5:  Solving Systems with Cramer's Rule","rendered":"Solutions 2.5:  Solving Systems with Cramer&#8217;s Rule"},"content":{"raw":"<h2>Solutions to Try Its<\/h2>\r\n1.\u00a0[latex]\\left(3,-7\\right)[\/latex]\r\n\r\n2.\u00a0[latex]-10[\/latex]\r\n\r\n3.\u00a0[latex]\\left(-2,\\frac{3}{5},\\frac{12}{5}\\right)[\/latex]\r\n<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]\r\n\r\n49.\u00a0Yes; 18, 38\r\n\r\n51.\u00a0Yes; 33, 36, 37\r\n\r\n53.\u00a0$7,000 in first account, $3,000 in second account.\r\n\r\n55.\u00a0120 children, 1,080 adult\r\n\r\n57.\u00a04 gal yellow, 6 gal blue\r\n\r\n59.\u00a013 green tomatoes, 17 red tomatoes\r\n\r\n61.\u00a0Strawberries 18%, oranges 9%, kiwi 10%\r\n\r\n63.\u00a0100 for movie 1, 230 for movie 2, 312 for movie 3\r\n\r\n65.\u00a020\u201329: 2,100, 30\u201339: 2,600, 40\u201349: 825\r\n\r\n67.\u00a0300 almonds, 400 cranberries, 300 cashews","rendered":"<h2>Solutions to Try Its<\/h2>\n<p>1.\u00a0[latex]\\left(3,-7\\right)[\/latex]<\/p>\n<p>2.\u00a0[latex]-10[\/latex]<\/p>\n<p>3.\u00a0[latex]\\left(-2,\\frac{3}{5},\\frac{12}{5}\\right)[\/latex]<\/p>\n<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<p>49.\u00a0Yes; 18, 38<\/p>\n<p>51.\u00a0Yes; 33, 36, 37<\/p>\n<p>53.\u00a0$7,000 in first account, $3,000 in second account.<\/p>\n<p>55.\u00a0120 children, 1,080 adult<\/p>\n<p>57.\u00a04 gal yellow, 6 gal blue<\/p>\n<p>59.\u00a013 green tomatoes, 17 red tomatoes<\/p>\n<p>61.\u00a0Strawberries 18%, oranges 9%, kiwi 10%<\/p>\n<p>63.\u00a0100 for movie 1, 230 for movie 2, 312 for movie 3<\/p>\n<p>65.\u00a020\u201329: 2,100, 30\u201339: 2,600, 40\u201349: 825<\/p>\n<p>67.\u00a0300 almonds, 400 cranberries, 300 cashews<\/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":6,"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":14214,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/14226","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/users\/23485"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/14226\/revisions"}],"predecessor-version":[{"id":15237,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/14226\/revisions\/15237"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/parts\/14214"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/14226\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/media?parent=14226"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapter-type?post=14226"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/contributor?post=14226"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/license?post=14226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}