{"id":3194,"date":"2025-08-15T22:34:10","date_gmt":"2025-08-15T22:34:10","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=3194"},"modified":"2025-09-23T16:37:33","modified_gmt":"2025-09-23T16:37:33","slug":"solving-systems-with-inverses-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/solving-systems-with-inverses-apply-it\/","title":{"raw":"Solving Systems with Inverses: Apply It","rendered":"Solving Systems with Inverses: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Find the inverse of a matrix.<\/li>\r\n \t<li>Solve a system of linear equations using an inverse matrix.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<div>\r\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\r\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\r\n<p class=\"whitespace-normal break-words\">Alex is a college junior who manages two different income sources while maintaining their academic performance. They tutor high school students and deliver food through a delivery app, while also needing to balance dedicated time for classes and studying. Each activity has different time requirements and scheduling constraints. Using matrix methods helps them optimize their schedule to meet financial goals while succeeding academically.<\/p>\r\n\r\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">The Time Management Challenge<\/h2>\r\n<p class=\"whitespace-normal break-words\">Alex needs to strategically allocate their available hours across three priorities: work income, work flexibility, and academic success.<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]312577[\/ohm_question]<\/p>\r\n\r\n<\/section>Let's try another context with income goals factored in.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312632[\/ohm_question]<\/section><\/div>\r\n<\/div>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Find the inverse of a matrix.<\/li>\n<li>Solve a system of linear equations using an inverse matrix.<\/li>\n<\/ul>\n<\/section>\n<div>\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\n<p class=\"whitespace-normal break-words\">Alex is a college junior who manages two different income sources while maintaining their academic performance. They tutor high school students and deliver food through a delivery app, while also needing to balance dedicated time for classes and studying. Each activity has different time requirements and scheduling constraints. Using matrix methods helps them optimize their schedule to meet financial goals while succeeding academically.<\/p>\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">The Time Management Challenge<\/h2>\n<p class=\"whitespace-normal break-words\">Alex needs to strategically allocate their available hours across three priorities: work income, work flexibility, and academic success.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm312577\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312577&theme=lumen&iframe_resize_id=ohm312577&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<p>Let&#8217;s try another context with income goals factored in.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312632\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312632&theme=lumen&iframe_resize_id=ohm312632&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":67,"menu_order":19,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":514,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3194"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":6,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3194\/revisions"}],"predecessor-version":[{"id":4288,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3194\/revisions\/4288"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/514"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3194\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=3194"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=3194"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=3194"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=3194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}