{"id":20016,"date":"2024-04-15T05:47:15","date_gmt":"2024-04-15T05:47:15","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20016"},"modified":"2024-04-15T05:47:15","modified_gmt":"2024-04-15T05:47:15","slug":"consider-the-matrix-as-given-below-left-beginarray20c-123-047-003-endarray-right-which-one-of-the-following-options-provides-the-correct-values-of-the-eig","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-matrix-as-given-below-left-beginarray20c-123-047-003-endarray-right-which-one-of-the-following-options-provides-the-correct-values-of-the-eig\/","title":{"rendered":"Consider the matrix as given below: \\[\\left[ {\\begin{array}{*{20}{c}} 1&#038;2&#038;3 \\\\ 0&#038;4&#038;7 \\\\ 0&#038;0&#038;3 \\end{array}} \\right]\\] Which one of the following options provides the CORRECT values of the eigen values of the matrix? A. 1, 4. 3 B. 3, 7, 3 C. 7, 3, 2 D. 1, 2, 3"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;1, 4. 3&#8243; option2=&#8221;3, 7, 3&#8243; option3=&#8221;7, 3, 2&#8243; option4=&#8221;1, 2, 3&#8243; correct=&#8221;option3&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{\\text{A}}$.<\/p>\n<p>The eigenvalues of a matrix are the roots of its characteristic polynomial. The characteristic polynomial of a matrix $A$ is given by $$p(x) = |xI &#8211; A|.$$<\/p>\n<p>In this case, we have $$p(x) = |xI &#8211; A| = \\begin{vmatrix} x &#8211; 1 &amp; 2 &amp; 3 \\\\ 0 &amp; x &#8211; 4 &amp; 7 \\\\ 0 &amp; 0 &amp; x &#8211; 3 \\end{vmatrix} = (x &#8211; 1)(x &#8211; 4)(x &#8211; 3).$$<\/p>\n<p>Therefore, the eigenvalues of the matrix are $1$, $4$, and $3$.<\/p>\n<p>Option A is the only option that contains all three of these eigenvalues.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;1, 4. 3&#8243; option2=&#8221;3, 7, 3&#8243; option3=&#8221;7, 3, 2&#8243; option4=&#8221;1, 2, 3&#8243; correct=&#8221;option3&#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":[],"class_list":["post-20016","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"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>Consider the matrix as given below: \\[\\left[ {\\begin{array}{*{20}{c}} 1&amp;2&amp;3 \\\\ 0&amp;4&amp;7 \\\\ 0&amp;0&amp;3 \\end{array}} \\right]\\] Which one of the following options provides the CORRECT values of the eigen values of the matrix? 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A. 1, 4. 3 B. 3, 7, 3 C. 7, 3, 2 D. 1, 2, 3","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\/consider-the-matrix-as-given-below-left-beginarray20c-123-047-003-endarray-right-which-one-of-the-following-options-provides-the-correct-values-of-the-eig\/","og_locale":"en_US","og_type":"article","og_title":"Consider the matrix as given below: \\[\\left[ {\\begin{array}{*{20}{c}} 1&2&3 \\\\ 0&4&7 \\\\ 0&0&3 \\end{array}} \\right]\\] Which one of the following options provides the CORRECT values of the eigen values of the matrix? 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