{"id":1792,"date":"2015-11-12T18:30:44","date_gmt":"2015-11-12T18:30:44","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1792"},"modified":"2015-11-12T18:30:44","modified_gmt":"2015-11-12T18:30:44","slug":"key-concepts-glossary-28","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/key-concepts-glossary-28\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2>Key Concepts<\/h2>\n<ul><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><h2>Glossary<\/h2>\n<dl id=\"fs-id1165134073074\" class=\"definition\"><dt>column<\/dt><dd id=\"fs-id1165134073079\">a set of numbers aligned vertically in a matrix<\/dd><\/dl><dl id=\"fs-id1165135639171\" class=\"definition\"><dt>entry<\/dt><dd id=\"fs-id1165135639177\">an element, coefficient, or constant in a matrix<\/dd><\/dl><dl id=\"fs-id1165135639180\" class=\"definition\"><dt>matrix<\/dt><dd id=\"fs-id1165137937501\">a rectangular array of numbers<\/dd><\/dl><dl id=\"fs-id1165134033250\" class=\"definition\"><dt>row<\/dt><dd id=\"fs-id1165137937510\">a set of numbers aligned horizontally in a matrix<\/dd><\/dl><dl id=\"fs-id1165135199312\" class=\"definition\"><dt>scalar multiple<\/dt><dd id=\"fs-id1165135199316\">an entry of a matrix that has been multiplied by a scalar<\/dd><\/dl>","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-id1165134073074\" class=\"definition\">\n<dt>column<\/dt>\n<dd id=\"fs-id1165134073079\">a set of numbers aligned vertically in a matrix<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135639171\" class=\"definition\">\n<dt>entry<\/dt>\n<dd id=\"fs-id1165135639177\">an element, coefficient, or constant in a matrix<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135639180\" class=\"definition\">\n<dt>matrix<\/dt>\n<dd id=\"fs-id1165137937501\">a rectangular array of numbers<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134033250\" class=\"definition\">\n<dt>row<\/dt>\n<dd id=\"fs-id1165137937510\">a set of numbers aligned horizontally in a matrix<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135199312\" class=\"definition\">\n<dt>scalar multiple<\/dt>\n<dd id=\"fs-id1165135199316\">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-1792\">\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 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