{"id":2664,"date":"2025-08-13T18:24:21","date_gmt":"2025-08-13T18:24:21","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2664"},"modified":"2025-12-03T18:40:21","modified_gmt":"2025-12-03T18:40:21","slug":"matrices-and-matrix-operations-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/matrices-and-matrix-operations-background-youll-need-2\/","title":{"raw":"Matrices and Matrix Operations: Background You'll Need 2","rendered":"Matrices and Matrix Operations: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Identify rows and columns<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p data-start=\"203\" data-end=\"409\">Before working with matrices, it\u2019s important to understand the basic structure of how they are organized. A <strong data-start=\"311\" data-end=\"321\">matrix<\/strong> is a rectangular arrangement of numbers, symbols, or expressions in rows and columns.<\/p>\r\n\r\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<h3>rows x columns<\/h3>\r\n<ul>\r\n \t<li>Rows go across (horizontally)<\/li>\r\n \t<li>Columns go up and down (vertically)<\/li>\r\n<\/ul>\r\n<img class=\"aligncenter wp-image-5022\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/03183746\/10.B.2.Diagram-300x139.png\" alt=\"A diagram showing a 3-by-3 matrix with its three rows highlighted horizontally on the left and the same matrix with its three columns highlighted vertically on the right.\" width=\"574\" height=\"266\" \/>\r\n\r\n<\/section><section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<div>\r\n<h3>element<\/h3>\r\nEach value in a matrix is called an element.\r\n\r\n&nbsp;\r\n\r\nThe number of elements can be found by calculating [latex]rows \\times columns[\/latex]\r\n\r\n<\/div>\r\n<\/section>&nbsp;\r\n\r\n<section class=\"textbox example\" aria-label=\"Example\">Identify the number of rows, columns, and elements in the matrix:\\begin{bmatrix}\r\n2 &amp; 5 &amp; 7 \\\\\r\n4 &amp; 0 &amp; -1\r\n\\end{bmatrix}[reveal-answer q=\"723965\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"723965\"]There are two rows, three columns, and six elements in the matrix.[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312374[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Identify rows and columns<\/li>\n<\/ul>\n<\/section>\n<p data-start=\"203\" data-end=\"409\">Before working with matrices, it\u2019s important to understand the basic structure of how they are organized. A <strong data-start=\"311\" data-end=\"321\">matrix<\/strong> is a rectangular arrangement of numbers, symbols, or expressions in rows and columns.<\/p>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<h3>rows x columns<\/h3>\n<ul>\n<li>Rows go across (horizontally)<\/li>\n<li>Columns go up and down (vertically)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5022\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/03183746\/10.B.2.Diagram-300x139.png\" alt=\"A diagram showing a 3-by-3 matrix with its three rows highlighted horizontally on the left and the same matrix with its three columns highlighted vertically on the right.\" width=\"574\" height=\"266\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/03183746\/10.B.2.Diagram-300x139.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/03183746\/10.B.2.Diagram-65x30.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/03183746\/10.B.2.Diagram-225x105.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/03183746\/10.B.2.Diagram-350x163.png 350w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/03183746\/10.B.2.Diagram.png 669w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<\/section>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<div>\n<h3>element<\/h3>\n<p>Each value in a matrix is called an element.<\/p>\n<p>&nbsp;<\/p>\n<p>The number of elements can be found by calculating [latex]rows \\times columns[\/latex]<\/p>\n<\/div>\n<\/section>\n<p>&nbsp;<\/p>\n<section class=\"textbox example\" aria-label=\"Example\">Identify the number of rows, columns, and elements in the matrix:\\begin{bmatrix}<br \/>\n2 &amp; 5 &amp; 7 \\\\<br \/>\n4 &amp; 0 &amp; -1<br \/>\n\\end{bmatrix}<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q723965\">Show Solution<\/button><\/p>\n<div id=\"q723965\" class=\"hidden-answer\" style=\"display: none\">There are two rows, three columns, and six elements in the matrix.<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312374\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312374&theme=lumen&iframe_resize_id=ohm312374&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":67,"menu_order":3,"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":"background_you_need","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\/2664"}],"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\/2664\/revisions"}],"predecessor-version":[{"id":5024,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2664\/revisions\/5024"}],"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\/2664\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2664"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2664"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2664"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2664"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}