{"id":20051,"date":"2024-04-15T05:47:42","date_gmt":"2024-04-15T05:47:42","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20051"},"modified":"2024-04-15T05:47:42","modified_gmt":"2024-04-15T05:47:42","slug":"the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/","title":{"rendered":"The matrix \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} {\\frac{3}{2}}&#038;0&#038;{\\frac{1}{2}} \\\\ 0&#038;{ &#8211; 1}&#038;0 \\\\ {\\frac{1}{2}}&#038;0&#038;{\\frac{3}{2}} \\end{array}} \\right]\\] has three distinct eigen values and one of its eigen vectors is \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ 1 \\end{array}} \\right].\\] Which one of the following can be another eigen vector of A? A. \\[\\left[ {\\begin{array}{*{20}{c}} 0 \\\\ 0 \\\\ { &#8211; 1} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1} \\\\ 0 \\\\ 0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ { &#8211; 1} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ { &#8211; 1} \\\\ 1 \\end{array}} \\right]\\]"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a9b29bcd0896\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    &#8221;[left[                <\/div>\r\n                                                                                                                                                                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    \\]&#8221; option2=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1} \\\\ 0 \\\\ 0 \\end{array}} \\right]\\]&#8221; option3=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ { &#8211; 1} \\end{array}} \\right]\\]&#8221; option4=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ { &#8211; 1} \\\\ 1 \\end{array}} \\right]\\]&#8221; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{\\left[ {\\begin{array}{*{20}{c}} 1 \\ 0 \\ { &#8211; 1} \\end{array}} \\right]}$.<\/p>\n<p>An eigenvector of a matrix $A$ is a nonzero vector $v$ such that $Av=\\lambda v$ for some scalar $\\lambda$. In other words, an eigenvector is a vector that is scaled by a constant when it is multiplied by $A$.<\/p>\n<p>The matrix $A$ has three distinct eigenvalues, which means that it has three linearly independent eigenvectors. One of these <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> eigenvectors is $\\left[ {\\begin{array}{*{20}{c}} 1 \\ 0 \\ 1 \\end{array}} \\right]$.<\/p>\n<p>To find another eigenvector of $A$, we can use the following procedure:<\/p>\n<ol>\n<li>Let $v$ be a vector that is not a scalar multiple of $\\left[ {\\begin{array}{*{20}{c}} 1 \\ 0 \\ 1 \\end{array}} \\right]$.<\/li>\n<li>Multiply $v$ by $A$ to get $Av$.<\/li>\n<li>Solve the equation $Av=\\lambda v$ for $\\lambda$.<\/li>\n<li>If $\\lambda$ is an eigenvalue of $A$, then $v$ is an eigenvector of $A$ corresponding to $\\lambda$.<\/li>\n<\/ol>\n<p>In this case, we can let $v=\\left[ {\\begin{array}{*{20}{c}} x \\ y \\ z \\end{array}} \\right]$. Multiplying $v$ by $A$, we get<\/p>\n<p>[Av=\\left[ {\\begin{array}{<em>{20}{c}} {\\frac{3}{2}}x&amp;0&amp;{\\frac{1}{2}}y \\ 0&amp;{ &#8211; 1}y&amp;0 \\ {\\frac{1}{2}}z&amp;0&amp;{\\frac{3}{2}}z \\end{array}} \\right]\\left[ {\\begin{array}{<\/em>{20}{c}} x \\ y \\ z \\end{array}} \\right]=\\left[ {\\begin{array}{*{20}{c}} {\\frac{3}{2}}x-\\frac{1}{2}yz \\ -y \\ \\frac{3}{2}z-\\frac{1}{2}xy \\end{array}} \\right]]<\/p>\n<p>Solving the equation $Av=\\lambda <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> v$ for $\\lambda$, we get<\/p>\n<p>[\\left[ {\\begin{array}{<em>{20}{c}} {\\frac{3}{2}}x-\\frac{1}{2}yz \\ -y \\ \\frac{3}{2}z-\\frac{1}{2}xy \\end{array}} \\right]=\\lambda \\left[ {\\begin{array}{<\/em>{20}{c}} x \\ y \\ z \\end{array}} \\right]]<\/p>\n<p>This gives us the system of equations<\/p>\n<p>\\begin{align<em>}<br \/>\n{\\frac{3}{2}}x-\\frac{1}{2}yz &amp;= \\lambda x \\<br \/>\n-y &amp;= \\lambda y \\<br \/>\n\\frac{3}{2}z-\\frac{1}{2}xy &amp;= \\lambda z<br \/>\n\\end{align<\/em>}<\/p>\n<p>Solving this system of equations, we get<\/p>\n<p>\\begin{align<em>}<br \/>\nx &amp;= \\frac{2\\lambda}{3+z} \\<br \/>\ny &amp;= \\frac{2\\lambda}{3} \\<br \/>\nz &amp;= \\frac{2\\lambda}{3-x}<br \/>\n\\end{align<\/em>}<\/p>\n<p>Therefore, an eigenvector of $A$ corresponding to the eigenvalue $\\lambda$ is<\/p>\n<p>[\\left[ {\\begin{array}{*{20}{c}} \\frac{2\\lambda}{3+z} \\ \\frac{2\\lambda}{3} \\ \\frac{2\\lambda}{3-x} \\end{array}} \\right]]<\/p>\n<p>For $\\lambda=1$, this gives us the eigenvector $\\left[ {\\begin{array}{*{20}{c}} 1 \\ 0 \\ -1 \\end{array}} \\right]$.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\\]&#8221; option2=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1} \\\\ 0 \\\\ 0 \\end{array}} \\right]\\]&#8221; option3=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ { &#8211; 1} \\end{array}} \\right]\\]&#8221; Subscribe on YouTube option4=&#8221;\\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ { &#8211; 1} \\\\ 1 \\end{array}} \\right]\\]&#8221; correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[489],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The matrix \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} {\\frac{3}{2}}&amp;0&amp;{\\frac{1}{2}} \\\\ 0&amp;{ - 1}&amp;0 \\\\ {\\frac{1}{2}}&amp;0&amp;{\\frac{3}{2}} \\end{array}} \\right]\\] has three distinct eigen values and one of its eigen vectors is \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ 1 \\end{array}} \\right].\\] Which one of the following can be another eigen vector of A? A. \\[\\left[ {\\begin{array}{*{20}{c}} 0 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1} \\\\ 0 \\\\ 0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ { - 1} \\\\ 1 \\end{array}} \\right]\\]<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The matrix \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} {\\frac{3}{2}}&amp;0&amp;{\\frac{1}{2}} \\\\ 0&amp;{ - 1}&amp;0 \\\\ {\\frac{1}{2}}&amp;0&amp;{\\frac{3}{2}} \\end{array}} \\right]\\] has three distinct eigen values and one of its eigen vectors is \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ 1 \\end{array}} \\right].\\] Which one of the following can be another eigen vector of A? A. \\[\\left[ {\\begin{array}{*{20}{c}} 0 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1} \\\\ 0 \\\\ 0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ { - 1} \\\\ 1 \\end{array}} \\right]\\]\" \/>\n<meta property=\"og:description\" content=\"]&#8221; option2=&#8221;[left[ {begin{array}{*{20}{c}} { &#8211; 1} \\ 0 \\ 0 end{array}} right]]&#8221; option3=&#8221;[left[ {begin{array}{*{20}{c}} 1 \\ 0 \\ { &#8211; 1} end{array}} right]]&#8221; option4=&#8221;[left[ {begin{array}{*{20}{c}} Subscribe on YouTube 1 \\ { &#8211; 1} \\ 1 end{array}} right]]&#8221; correct=&#8221;option1&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T05:47:42+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The matrix \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} {\\frac{3}{2}}&0&{\\frac{1}{2}} \\\\ 0&{ - 1}&0 \\\\ {\\frac{1}{2}}&0&{\\frac{3}{2}} \\end{array}} \\right]\\] has three distinct eigen values and one of its eigen vectors is \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ 1 \\end{array}} \\right].\\] Which one of the following can be another eigen vector of A? A. \\[\\left[ {\\begin{array}{*{20}{c}} 0 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1} \\\\ 0 \\\\ 0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ { - 1} \\\\ 1 \\end{array}} \\right]\\]","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/","og_locale":"en_US","og_type":"article","og_title":"The matrix \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} {\\frac{3}{2}}&0&{\\frac{1}{2}} \\\\ 0&{ - 1}&0 \\\\ {\\frac{1}{2}}&0&{\\frac{3}{2}} \\end{array}} \\right]\\] has three distinct eigen values and one of its eigen vectors is \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ 1 \\end{array}} \\right].\\] Which one of the following can be another eigen vector of A? A. \\[\\left[ {\\begin{array}{*{20}{c}} 0 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1} \\\\ 0 \\\\ 0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ { - 1} \\\\ 1 \\end{array}} \\right]\\]","og_description":"]&#8221; option2=&#8221;[left[ {begin{array}{*{20}{c}} { &#8211; 1} \\ 0 \\ 0 end{array}} right]]&#8221; option3=&#8221;[left[ {begin{array}{*{20}{c}} 1 \\ 0 \\ { &#8211; 1} end{array}} right]]&#8221; option4=&#8221;[left[ {begin{array}{*{20}{c}} Subscribe on YouTube 1 \\ { &#8211; 1} \\ 1 end{array}} right]]&#8221; correct=&#8221;option1&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T05:47:42+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/","name":"The matrix \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} {\\frac{3}{2}}&0&{\\frac{1}{2}} \\\\ 0&{ - 1}&0 \\\\ {\\frac{1}{2}}&0&{\\frac{3}{2}} \\end{array}} \\right]\\] has three distinct eigen values and one of its eigen vectors is \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ 1 \\end{array}} \\right].\\] Which one of the following can be another eigen vector of A? A. \\[\\left[ {\\begin{array}{*{20}{c}} 0 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} { - 1} \\\\ 0 \\\\ 0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ { - 1} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ { - 1} \\\\ 1 \\end{array}} \\right]\\]","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T05:47:42+00:00","dateModified":"2024-04-15T05:47:42+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-matrix-texta-left-beginarray20c-frac320frac12-0-10-frac120frac32-endarray-right-has-three-distinct-eigen-va\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Linear Algebra","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/linear-algebra\/"},{"@type":"ListItem","position":4,"name":"The matrix \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} {\\frac{3}{2}}&#038;0&#038;{\\frac{1}{2}} \\\\ 0&#038;{ &#8211; 1}&#038;0 \\\\ {\\frac{1}{2}}&#038;0&#038;{\\frac{3}{2}} \\end{array}} \\right]\\] has three distinct eigen values and one of its eigen vectors is \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ 1 \\end{array}} \\right].\\] Which one of the following can be another eigen vector of A? A. \\[\\left[ {\\begin{array}{*{20}{c}} 0 \\\\ 0 \\\\ { &#8211; 1} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} { &#8211; 1} \\\\ 0 \\\\ 0 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ 0 \\\\ { &#8211; 1} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} 1 \\\\ { &#8211; 1} \\\\ 1 \\end{array}} \\right]\\]"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/20051"}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=20051"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/20051\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=20051"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=20051"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=20051"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}