{"id":20000,"date":"2024-04-15T05:47:02","date_gmt":"2024-04-15T05:47:02","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20000"},"modified":"2024-04-15T05:47:02","modified_gmt":"2024-04-15T05:47:02","slug":"the-sum-of-eigen-values-of-matrix-m-is-where-left-textm-right-left-beginarray20c-215650795-655150835-485355550-endarray-righ","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-sum-of-eigen-values-of-matrix-m-is-where-left-textm-right-left-beginarray20c-215650795-655150835-485355550-endarray-righ\/","title":{"rendered":"The sum of Eigen values of matrix, [M] is where \\[\\left[ {\\text{M}} \\right] = \\left[ {\\begin{array}{*{20}{c}} {215}&#038;{650}&#038;{795} \\\\ {655}&#038;{150}&#038;{835} \\\\ {485}&#038;{355}&#038;{550} \\end{array}} \\right]\\] A. 915 B. 1355 C. 1640 D. 2180"},"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_6a9934354f344\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    915                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    1355                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    1640                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    2180                <\/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    <!--more--><\/p>\n<p>The sum of the eigenvalues of a matrix is equal to the trace of the matrix. The trace of a matrix is the sum of the elements <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> on the main diagonal. In this case, the matrix is $\\left[ {\\text{M}} \\right] = \\left[ {\\begin{array}{*{20}{c}} {215}&amp;{650}&amp;{795} \\ {655}&amp;{150}&amp;{835} \\ {485}&amp;{355}&amp;{550} \\end{array}} \\right]$. The trace of this matrix is $215 + 150 + 550 = 915$. Therefore, the sum <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> of the eigenvalues of this matrix is $\\boxed{915}$.<\/p>\n<p>Here is a brief explanation of each option:<\/p>\n<ul>\n<li>Option A: $915$ is the correct answer.<\/li>\n<li>Option B: $1355$ is the sum of the elements on the first and third rows of the matrix. However, the sum of the eigenvalues is not equal to the sum of the elements on any row or column of the matrix.<\/li>\n<li>Option C: $1640$ is the sum of the elements on the main diagonal of the matrix. However, the sum of the eigenvalues is not equal to the sum of the elements on the main diagonal.<\/li>\n<li>Option D: $2180$ is the sum of the squares of the elements on the main diagonal of the matrix. However, the sum of the eigenvalues is not equal to the sum of the squares of the elements on the main diagonal.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Subscribe on YouTube<\/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 sum of Eigen values of matrix, [M] is where \\[\\left[ {\\text{M}} \\right] = \\left[ {\\begin{array}{*{20}{c}} {215}&amp;{650}&amp;{795} \\\\ {655}&amp;{150}&amp;{835} \\\\ {485}&amp;{355}&amp;{550} \\end{array}} \\right]\\] A. 915 B. 1355 C. 1640 D. 2180<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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