[amp_mcq option1=”2″ option2=”4″ option3=”6″ option4=”8″ correct=”option3″]<\/p>\n
The correct answer is $\\boxed{4}$.<\/p>\n
To find the eigenvalues of a matrix, we can use the following formula:<\/p>\n
$$\\lambda = \\frac{tr(A) – \\det(A)}{2}$$<\/p>\n
where $tr(A)$ is the trace of $A$ and $\\det(A)$ is the determinant of $A$.<\/p>\n
In this case, we have:<\/p>\n
$$tr(A) = 4 + 4 = 8$$<\/p>\n
$$\\det(A) = 4^2 – 2 \\cdot 4 \\cdot 2 = 0$$<\/p>\n
Therefore, the eigenvalues of $A$ are $\\frac{8 – 0}{2} = 4$.<\/p>\n
To find the eigenvector corresponding to the eigenvalue $\\lambda = 4$, we can use the following formula:<\/p>\n
$$v = \\frac{1}{\\det(A – \\lambda I)}(A – \\lambda I)u$$<\/p>\n
where $u$ is any non-zero vector.<\/p>\n
In this case, we can choose $u = \\left[ {\\begin{array}{*{20}{c}} {101} \\ {101} \\end{array}} \\right]$.<\/p>\n
Therefore, the eigenvector corresponding to the eigenvalue $\\lambda = 4$ is $\\boxed{\\left[ {\\begin{array}{*{20}{c}} {101} \\ {101} \\end{array}} \\right]}$.<\/p>\n
Here is a brief explanation of each option:<\/p>\n
[amp_mcq option1=”2″ option2=”4″ option3=”6″ option4=”8″ correct=”option3″]<\/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-19989","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"yoast_head":"\n