{"id":8292,"date":"2024-01-14T21:21:16","date_gmt":"2024-01-14T21:21:16","guid":{"rendered":"https:\/\/assignment.essayshark.com\/blog\/?p=8292"},"modified":"2024-04-23T07:46:19","modified_gmt":"2024-04-23T07:46:19","slug":"eigenvalues-and-eigenvectors-of-3x3-matrix-example","status":"publish","type":"post","link":"https:\/\/assignmentshark.com\/blog\/eigenvalues-and-eigenvectors-of-3x3-matrix-example\/","title":{"rendered":"Eigenvalues and Eigenvectors of 3&#215;3 Matrix Example"},"content":{"rendered":"<p><b>Task:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Find the eigenvectors and eigenvalues of the following matrix:<\/span><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8318\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen1.png\" alt=\"\" width=\"225\" height=\"165\" \/><\/a><\/p>\n<p><!--more--><\/p>\n<p><b>Solution:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">To find eigenvectors we must solve the equation below for each eigenvalue:<\/span><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8316\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen2.png\" alt=\"\" width=\"223\" height=\"82\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\">The eigenvalues are the roots of the characteristic equation:<\/span><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen10.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-8300\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen10-300x146.png\" alt=\"\" width=\"300\" height=\"146\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen10-300x146.png 300w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen10.png 318w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen3-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8322 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen3-1.png\" alt=\"\" width=\"963\" height=\"321\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen3-1.png 963w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen3-1-300x100.png 300w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen3-1-768x256.png 768w\" sizes=\"auto, (max-width: 963px) 100vw, 963px\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\">The solutions of the equation above are eigenvalues and they are equal to:<\/span><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen4.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8312 \" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen4.png\" alt=\"\" width=\"246\" height=\"65\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen4.png 318w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen4-300x79.png 300w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\">Eigenvectors for:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen5.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8310 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen5.png\" alt=\"\" width=\"910\" height=\"335\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen5.png 910w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen5-300x110.png 300w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen5-768x283.png 768w\" sizes=\"auto, (max-width: 910px) 100vw, 910px\" \/><\/a><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Now we must solve the following equation:<\/span><\/p>\n<p><b><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen6.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8308 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen6.png\" alt=\"\" width=\"344\" height=\"212\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen6.png 344w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen6-300x185.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/a><br \/>\nFirst let\u2019s reduce the matrix:<\/b><\/p>\n<p><b> <a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen14.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8294 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen14.png\" alt=\"\" width=\"328\" height=\"248\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen14.png 328w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen14-300x227.png 300w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/a> <a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen7-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8324 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen7-1.png\" alt=\"\" width=\"316\" height=\"794\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen7-1.png 316w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen7-1-119x300.png 119w\" sizes=\"auto, (max-width: 316px) 100vw, 316px\" \/><\/a>\u00a0\u00a0\u00a0\u00a0<\/b><\/p>\n<p><b>This reduces to the equation:<\/b><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen8.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8304 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen8.png\" alt=\"\" width=\"265\" height=\"159\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\">Eigenvectors for:<\/span><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen9.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8302 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen9.png\" alt=\"\" width=\"785\" height=\"227\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen9.png 785w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen9-300x87.png 300w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen9-768x222.png 768w\" sizes=\"auto, (max-width: 785px) 100vw, 785px\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\">Now we must solve the following equation:<\/span><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen10.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8300 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen10.png\" alt=\"\" width=\"318\" height=\"155\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen10.png 318w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen10-300x146.png 300w\" sizes=\"auto, (max-width: 318px) 100vw, 318px\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\">First let\u2019s reduce the matrix:<\/span><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen11.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8298 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen11.png\" alt=\"\" width=\"283\" height=\"562\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen11.png 283w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen11-151x300.png 151w\" sizes=\"auto, (max-width: 283px) 100vw, 283px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen13.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8328 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen13.png\" alt=\"\" width=\"265\" height=\"821\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen13.png 265w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen13-97x300.png 97w\" sizes=\"auto, (max-width: 265px) 100vw, 265px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">This reduces to the equation:<\/span><\/p>\n<p><a href=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen14.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-8294 size-full\" src=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen14.png\" alt=\"\" width=\"328\" height=\"248\" srcset=\"https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen14.png 328w, https:\/\/assignmentshark.com\/blog\/wp-content\/uploads\/2018\/03\/eigen14-300x227.png 300w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/a><\/p>\n<blockquote><p><i><span style=\"font-weight: 400;\">There are two kinds of students: those who love math and those who hate it. If you love it, our example of the solution to <\/span><\/i><i>eigenvalues and eigenvectors of 3&#215;3 matrix<\/i><i><span style=\"font-weight: 400;\"> will help you get a better understanding of it. This example was made by one of our experts; you can easily contact them if you are puzzled with complex tasks in math.<\/span><\/i><\/p><\/blockquote>\n<blockquote><p><i><span style=\"font-weight: 400;\">If you have trouble understanding your <\/span><\/i><i>eigenvalues and eigenvectors of 3&#215;3 matrix<\/i><i><span style=\"font-weight: 400;\"> assignment, there is no need to panic! Get professional help with your math assignment at any time that is convenient for you. We have gathered a team of experts in math who can easily solve even the most difficult math assignments. Improve your math skills with us!<\/span><\/i><\/p><\/blockquote>\n<blockquote><p><i><span style=\"font-weight: 400;\">AssignmentShark works day and night to provide expert help with assignments for students from all over the world. When you need prompt help, ask our professionals, as they are able to complete your assignment before the deadline. Also, to make our service affordable, we have provided reasonable prices so every student can afford our services. There is no time to wait for assistance! Get <a href=\"https:\/\/assignmentshark.com\/\" target=\"_blank\" rel=\"noopener\">assignment help online<\/a> done with our experts! <\/span><\/i><\/p><\/blockquote>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Task: Find the eigenvectors and eigenvalues of the following matrix:<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[55,35],"tags":[],"class_list":["post-8292","post","type-post","status-publish","format-standard","hentry","category-math","category-samples"],"_links":{"self":[{"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/posts\/8292","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/comments?post=8292"}],"version-history":[{"count":9,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/posts\/8292\/revisions"}],"predecessor-version":[{"id":12847,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/posts\/8292\/revisions\/12847"}],"wp:attachment":[{"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/media?parent=8292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/categories?post=8292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmentshark.com\/blog\/wp-json\/wp\/v2\/tags?post=8292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}