{"id":331,"date":"2023-06-21T13:22:57","date_gmt":"2023-06-21T13:22:57","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-matrices-and-matrix-operations\/"},"modified":"2023-06-21T13:22:57","modified_gmt":"2023-06-21T13:22:57","slug":"summary-matrices-and-matrix-operations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-matrices-and-matrix-operations\/","title":{"raw":"Summary: Matrices and Matrix Operations","rendered":"Summary: Matrices and Matrix Operations"},"content":{"raw":"\n\n<h2>Key Concepts<\/h2>\n<ul>\n \t<li>A matrix is a rectangular array of numbers. Entries are arranged in rows and columns.<\/li>\n \t<li>The dimensions of a matrix refer to the number of rows and the number of columns. A [latex]3\\times 2[\/latex] matrix has three rows and two columns.<\/li>\n \t<li>We add and subtract matrices of equal dimensions by adding and subtracting corresponding entries of each matrix.<\/li>\n \t<li>Scalar multiplication involves multiplying each entry in a matrix by a constant.<\/li>\n \t<li>Scalar multiplication is often required before addition or subtraction can occur.<\/li>\n \t<li>Multiplying matrices is possible when inner dimensions are the same\u2014the number of columns in the first matrix must match the number of rows in the second.<\/li>\n \t<li>The product of two matrices, [latex]A[\/latex] and [latex]B[\/latex], is obtained by multiplying each entry in row 1 of [latex]A[\/latex] by each entry in column 1 of [latex]B[\/latex]; then multiply each entry of row 1 of [latex]A[\/latex] by each entry in columns 2 of [latex]B,\\text{}[\/latex] and so on.<\/li>\n \t<li>Many real-world problems can often be solved using matrices.<\/li>\n \t<li>We can use a calculator to perform matrix operations after saving each matrix as a matrix variable.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong>column<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">a set of numbers aligned vertically in a matrix<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt><strong>entry<\/strong><\/dt>\n \t<dd id=\"fs-id1165133085665\">an element, coefficient, or constant in a matrix<\/dd>\n<\/dl>\n<\/dt>\n<\/dl>\n<\/dt>\n \t<dt>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong>matrix<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">a rectangular array of numbers<\/dd>\n<\/dl>\n<\/dt>\n<\/dl>\n<\/dt>\n<\/dl>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong>row<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">a set of numbers aligned horizontally in a matrix<\/dd>\n<\/dl>\n<\/dt>\n<\/dl>\n<\/dt>\n \t<dt>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n \t<dt>\n<dl id=\"fs-id1165137644987\" class=\"definition\">\n \t<dt><strong>scalar multiple<\/strong><\/dt>\n \t<dd id=\"fs-id1165137644990\">an entry of a matrix that has been multiplied by a scalar<\/dd>\n<\/dl>\n<\/dt>\n<\/dl>\n<\/dt>\n<\/dl>\n\n","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>A matrix is a rectangular array of numbers. Entries are arranged in rows and columns.<\/li>\n<li>The dimensions of a matrix refer to the number of rows and the number of columns. A [latex]3\\times 2[\/latex] matrix has three rows and two columns.<\/li>\n<li>We add and subtract matrices of equal dimensions by adding and subtracting corresponding entries of each matrix.<\/li>\n<li>Scalar multiplication involves multiplying each entry in a matrix by a constant.<\/li>\n<li>Scalar multiplication is often required before addition or subtraction can occur.<\/li>\n<li>Multiplying matrices is possible when inner dimensions are the same\u2014the number of columns in the first matrix must match the number of rows in the second.<\/li>\n<li>The product of two matrices, [latex]A[\/latex] and [latex]B[\/latex], is obtained by multiplying each entry in row 1 of [latex]A[\/latex] by each entry in column 1 of [latex]B[\/latex]; then multiply each entry of row 1 of [latex]A[\/latex] by each entry in columns 2 of [latex]B,\\text{}[\/latex] and so on.<\/li>\n<li>Many real-world problems can often be solved using matrices.<\/li>\n<li>We can use a calculator to perform matrix operations after saving each matrix as a matrix variable.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n<dt>\n<\/dt>\n<dt>\n<\/dt>\n<dt><strong>column<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">a set of numbers aligned vertically in a matrix<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n<dt><strong>entry<\/strong><\/dt>\n<dd id=\"fs-id1165133085665\">an element, coefficient, or constant in a matrix<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n<dt>\n<\/dt>\n<dt><strong>matrix<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">a rectangular array of numbers<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n<dt>\n<\/dt>\n<dt>\n<\/dt>\n<dt><strong>row<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">a set of numbers aligned horizontally in a matrix<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133085661\" class=\"definition\">\n<dt>\n<\/dt>\n<dt><strong>scalar multiple<\/strong><\/dt>\n<dd id=\"fs-id1165137644990\">an entry of a matrix that has been multiplied by a scalar<\/dd>\n<\/dl>\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-331\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/li><\/ul><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":395986,"menu_order":12,"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\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\"}]","CANDELA_OUTCOMES_GUID":"2fb87fbe-c67c-4068-9b0e-ae95eec362d2","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-331","chapter","type-chapter","status-publish","hentry"],"part":323,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/331","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/users\/395986"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/331\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/323"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/331\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=331"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=331"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=331"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}