For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal. (If not possible, enter IMPOSSIBLE.)A = 2 −2 9 0 3 −20 −1 2

Suppose that a 2×2 matrix A has an eigenvalue 2 with corresponding eigenvector [1 −1] and an eigenvalue −2 with corresponding eigenvector [3 −2]. Find an invertible matrix P and a diagonal matrix D so that A=PDP−1. Enter your answer as an equation of the form A=PDP−1. You must enter a number in every answer blank for the answer evaluator to work properly.

Time left 0:11:05Question 2Tries remaining: 2Marked out of 1.00Flag questionQuestion textDiagonalize the matrix [−1−425][−12−45].That is, find a diagonal matrix D𝐷 and an invertible matrix P𝑃 such that A=P⋅D⋅P−1

Let 3x3 matrix A=[-23 16 12/ -24 17 12/ -12 8 7]. Find an invertible matrix P and a diagonal matrix D such that D=P^(-1)AP.

A=（3,2,4 2,0,2 4,2,3） You are given that the characteristic equation of A is (λ + 1)2(λ − 8) = 0, i.e. the eigenvalues of A are λ = −1, 8. Find an orthogonal matrix P that orthogonally diagonalizes A

Let the matrix A =−1 0 00 0 01 0 1.(a) (5 pts) Why is A diagonalizeable?(b) (12 pts) Diagonalize A and find the invertible matrix P by which you diagonalized A.2