{"id":120,"date":"2022-04-13T10:03:41","date_gmt":"2022-04-13T10:03:41","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=120"},"modified":"2024-12-23T10:31:27","modified_gmt":"2024-12-23T10:31:27","slug":"f-1-matrix-vocabulary","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/f-1-matrix-vocabulary\/","title":{"rendered":"F.1 Matrix vocabulary"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00025c;text-transform:uppercase\"><strong>Matrices<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4dde4300b7763c9a2a860fe18546dfe2\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-foreground-color has-text-color\"><strong>Definition<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">A set of numbers or objects or symbols represented in the form of a rectangular array is called a matrix.&nbsp;<\/li>\n\n\n\n<li class=\"has-large-font-size\">The order of the matrix is defined by the number of rows and number of columns present in the rectangular array of representation.&nbsp;<\/li>\n\n\n\n<li class=\"has-large-font-size\">Unlike determinants, it has no value.<\/li>\n\n\n\n<li class=\"has-large-font-size\">A matrix of order m \u00d7 n,&nbsp;<strong>i.e.&nbsp;<\/strong>m rows and n columns, is represented below:<br><img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_cb1dca71-1ea8-4222-8fda-0f2338fe6d6f_lg.png?w=800&amp;dpr=1.0\" alt=\"Matrices: Overview\"><\/li>\n\n\n\n<li class=\"has-large-font-size\">Abbreviated as:&nbsp;A = &nbsp;[a<sub>ij<\/sub>]<sub>m \u00d7 n<\/sub>, where 1 \u2264 i \u2264 m; 1 \u2264 j \u2264 n, i denotes the row and j denotes the column.<\/li>\n\n\n\n<li class=\"has-large-font-size\">&nbsp;The number a<sub>11<\/sub>, a<sub>12<\/sub>, \u2026.. etc., are known as the elements of matrix A, where a<sub>ij&nbsp;<\/sub>belongs to the i<sup>th<\/sup>&nbsp;row and j<sup>th<\/sup>&nbsp;column and is called the (I,j)<sup>th<\/sup>&nbsp;element of the matrix A = [a<sub>ij<\/sub>].<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcTZW2izATBVLD6fuAwv1UZ9ZXezlockdC8k9A&amp;usqp=CAU\" alt=\"Matrices - Common Misconceptions\" style=\"aspect-ratio:1.7854077253218885;width:516px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading has-foreground-color has-text-color\"><strong>Type of Matrices<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Row Matrix:&nbsp;<\/strong>Matrix having one row&nbsp;<strong>i.e.<\/strong>&nbsp;matrix of order 1 \u00d7 n. They are also known as row vectors.\n<ul class=\"wp-block-list\">\n<li><strong>Example:&nbsp;<\/strong>A = &nbsp;[a<sub>11<\/sub>&nbsp;, a<sub>12<\/sub>, &#8230;&#8230; a<sub>1n<\/sub>]&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Column Matrix:&nbsp;<\/strong>Matrix having one column&nbsp;<strong>i.e.<\/strong>&nbsp;matrix of order m \u00d7 1. They are also known as column vectors.\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_45a9995d-d5a7-45b8-b255-08f75c77f0b2_lg.png?w=800&amp;dpr=1.0\" alt=\"Matrices: Overview\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Zero or Null Matrix:<\/strong>&nbsp;An m \u00d7 n &nbsp;matrix all whose entries are zero. It is denoted as O<sub>m\u00d7n<\/sub>.\n<ul class=\"wp-block-list\">\n<li><strong>Example:&nbsp;<img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_556db6ad-5a31-4812-8770-603102abd06b_lg.png?w=800&amp;dpr=1.0\" alt=\"Matrices: Overview\"><\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Horizontal Matrix:&nbsp;<\/strong>A matrix of order m \u00d7 n is a horizontal matrix if n &gt; m.\n<ul class=\"wp-block-list\">\n<li><strong>Example:&nbsp; <\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_03fb1cd6-bf50-4fca-b9a1-08a76687fa43_lg.png?w=800&amp;dpr=1.0\" alt=\"Matrices: Overview\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Vertical Matrix:&nbsp;<\/strong>A matrix of order m \u00d7 n is a vertical matrix if m &gt; n.\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong>&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_e281d9ed-6fcc-46d3-83d9-101441d20769_lg.png?w=800&amp;dpr=1.0\" alt=\"Matrices: Overview\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Square Matrix:&nbsp;<\/strong>If a number of rows is equal to a number of columns, then the matrix is a square matrix.\n<ul class=\"wp-block-list\">\n<li><strong>Example:&nbsp;<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_fafad6ca-0952-4564-b67f-eb9c751e421d_lg.png?w=800&amp;dpr=1.0\" alt=\"Matrices: Overview\"\/><\/figure><\/div>\n\n\n<figure class=\"wp-block-table has-large-font-size\"><table><tbody><tr><td><strong>\ud83d\udca1Note:<\/strong> In a square matrix,<br>&nbsp;<img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_adc91355-a625-435e-83a7-2082342c2334_lg.png?w=768&amp;dpr=1.0\" alt=\"Matrices: Overview\"><br><strong>(a)<\/strong> The pair of elements a<sub>ij<\/sub>&nbsp;&amp; a<sub>ji<\/sub>&nbsp;are called Conjugate Elements.<br><strong>Example:&nbsp;<\/strong>a<sub>12&nbsp;<\/sub>and a<sub>21<\/sub><br><strong>(b)&nbsp;<\/strong>The elements &nbsp;a<sub>11<\/sub>, a<sub>22<\/sub>, a<sub>33<\/sub>, &#8230;&#8230; a<sub>nn<\/sub>&nbsp;are called&nbsp;<strong>Diagonal Elements<\/strong>. The line along which the diagonal elements lie is called the &#8220;<strong>Principal or Leading<\/strong>&#8221; diagonal.<br><strong>(c)<\/strong>&nbsp;Sum of all the diagonal elements,&nbsp;<strong>i.e.&nbsp;<\/strong>\u03a3 a<sub>ii<\/sub>&nbsp;is known as trace of the matrix. It is denoted as t<sub>r<\/sub>(A).<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-large-font-size\"><strong>Diagonal Matrix:&nbsp;<\/strong>A square matrix in which all the elements are zero except the diagonal element. It is denoted as dia(d<sub>1<\/sub>, d<sub>2<\/sub>, &#8230;.., d<sub>n<\/sub>).<br><strong>Example:&nbsp; <\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_9dd46ea0-9daf-48f3-a36e-22cee18b69ad_lg.png?w=800&amp;dpr=1.0\" alt=\"Matrices: Overview\" style=\"width:249px;height:81px\"\/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"244\" height=\"206\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview.png\" alt=\"\" class=\"wp-image-11011\"\/><\/figure><\/div>\n\n\n<figure class=\"wp-block-table has-large-font-size\"><table><tbody><tr><td><strong>\ud83d\udca1<\/strong> <strong>Note:<\/strong><br>Min. number of zeros in a diagonal matrix of order n = n(n \u2013 1)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Scalar Matrix:&nbsp;<\/strong>A square matrix in which every non-diagonal element is zero and all diagonal elements are equal, is called a scalar matrix.<\/li>\n\n\n\n<li class=\"has-large-font-size\"><strong>i.e.<\/strong>&nbsp;in scalar matrix, a<sub>ij<\/sub>&nbsp;= 0, for i \u2260 j and a<sub>ij<\/sub>&nbsp;= k, for i = j\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> <\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_8cb56479-8d41-4973-a672-6baaee2c38cb_lg.png?w=800&amp;dpr=1.0\" alt=\"Matrices: Overview\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Unit\/Identity Matrix:<\/strong>&nbsp;A square matrix, in which every non-diagonal element is zero and every diagonal element is 1, is called, unit matrix or an identity matrix.<\/li>\n\n\n\n<li class=\"has-large-font-size\"><strong>i.e.<\/strong>&nbsp;in scalar matrix, a<sub>ij<\/sub>&nbsp;= 0, for i \u2260 j and a<sub>ij<\/sub>&nbsp;= 1, for i = j\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> <\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/edurev.gumlet.io\/ApplicationImages\/Temp\/8687595_61de4863-442f-4abc-8f79-4700c1ff45d6_lg.png?w=800&amp;dpr=1.0\" alt=\"Matrices: Overview\"\/><\/figure><\/div>\n\n\n<figure class=\"wp-block-table has-large-font-size\"><table><tbody><tr><td><strong>\ud83d\udca1<\/strong> <strong>Equality of Matrices&nbsp;<\/strong><br>A = [a<sub>ij<\/sub>] &amp; B = [b<sub>ij<\/sub>] will be equal, <br>only if <br>\ud83e\udd4fBoth have the same order<br>\ud83e\udd4fa<sub>i j<\/sub>&nbsp;= b<sub>i j&nbsp;<\/sub>&nbsp;for each pair of i &amp; j<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\">Learn with an example<\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f6a5a5\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-103a484386aad4118b515668f0b2b712\" style=\"color:#b00012\">what are the dimensions of this matrix ?<\/p>\n\n\n\n<p>[ 2  3  0]<\/p>\n\n\n\n<p>_____ by _____<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This matrix has 1 row and 3 columns, so the dimensions are 1 by 3.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d6f5e3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-d65860e0a894e702a6f55b5c168235e5\" style=\"color:#b00012\">Is this an identity matrix?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-16.png\" alt=\"\" class=\"wp-image-11018\" style=\"width:225px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-16.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-16-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-16-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-16-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p>Look at the given matrix.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"124\" height=\"93\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/17-removebg-preview-1.png\" alt=\"\" class=\"wp-image-7722\" style=\"width:185px;height:auto\"\/><\/figure>\n\n\n\n<p>This matrix has 1s on the diagonal from the top right to the bottom left instead of the diagonal from the top left to the bottom right, so it is not the identity matrix.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f1cdd7\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-6e4c49bc904395d2e1ef53975e3c4001\" style=\"color:#b00012\">Is this a row matrix?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-1-5.png\" alt=\"\" class=\"wp-image-11020\" style=\"width:248px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-1-5.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-1-5-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-1-5-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-1-5-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p>Look at the given matrix.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"83\" height=\"66\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/19-removebg-preview.png\" alt=\"\" class=\"wp-image-7726\" style=\"width:163px;height:auto\"\/><\/figure>\n\n\n\n<p>This matrix has 2 rows, so it is not a row matrix.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84187\/347\/295\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1.png\" alt=\"\" class=\"wp-image-3005\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/33695\/210\/226\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-1.png\" alt=\"\" class=\"wp-image-3007\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Matrices key notes: Definition Type of Matrices \ud83d\udca1Note: In a square matrix,&nbsp;(a) The pair of elements aij&nbsp;&amp; aji&nbsp;are called Conjugate Elements.Example:&nbsp;a12&nbsp;and a21(b)&nbsp;The elements &nbsp;a11, a22, a33, &#8230;&#8230; ann&nbsp;are called&nbsp;Diagonal Elements. The line along which the diagonal elements lie is called the &#8220;Principal or Leading&#8221; diagonal.(c)&nbsp;Sum of all the diagonal elements,&nbsp;i.e.&nbsp;\u03a3 aii&nbsp;is known as trace of<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/f-1-matrix-vocabulary\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.1 Matrix vocabulary&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-120","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/120","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=120"}],"version-history":[{"count":30,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/120\/revisions"}],"predecessor-version":[{"id":15498,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/120\/revisions\/15498"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}