[amp_mcq option1=”-3, -4″ option2=”-1, -2″ option3=”-1, -3″ option4=”-2, -4″ correct=”option3″]<\/p>\n
The correct answer is $\\boxed{\\text{B. }-1, -2}$.<\/p>\n
The eigenvalues of a matrix are the roots of its characteristic polynomial. The characteristic polynomial of a 2×2 matrix $A$ is given by $$p(x) = |xI – A| = x^2 – (tr(A))x + \\det(A).$$<\/p>\n
In this case, $A$ is a 2×2 matrix with eigenvalues $-2$ and $-3$. Therefore, its characteristic polynomial is $$p(x) = x^2 – (-2 – 3)x + (-2)(-3) = x^2 – 1x + 4.$$<\/p>\n
The eigenvalues of the matrix $(X + I)(X + 5I)$ are the roots of the polynomial $$p(x) = (x + 1)(x + 5) = x^2 + 6x + 5.$$<\/p>\n
Comparing the two polynomials, we see that the eigenvalues of $(X + I)(X + 5I)$ are $-1$ and $-2$.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”-3, -4″ option2=”-1, -2″ option3=”-1, -3″ option4=”-2, -4″ 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-20044","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"yoast_head":"\n