Intro to Linear Algebra - Chapter 5: Similarity

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Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A= PDP-1. A = A=PDP-1. Select one: O A . 141 1 1 P = 0 41 , D= 041 -101 -1 0 1 O B. 10-1 1 0 -1 P = 4 4 O, D= 4 4 0 1 1 1 1 O C. 1 0 10 0 P = 4 4 0 D = 4 40 0 1 01 1 O D. Not diagonalizableFind the matrix of the linear transformation T: V - W relative to B and C. Suppose B = {b1, b2} is a basis for V and C = {C1, C2, C3} is a basis for W. Let T be defined by T(b1) = -401 - 7c2 + 403 T(b2) = -4c1 - 14c2 + 503 Select one: O A . O B. O C. -4 -14 5 O D.For the given matrix A, find a basis for the corresponding eigenspace for the given eigenvalue. - 5 A = 5 5 ,A= -4 5 Select one: O A. O B. O C. O D.Define T: R2 - R2 by T(x) = Ax, where A is the matrix defined below. Find the requested basis B for R2 and the corresponding B-matrix for T. Find a basis B for R2 and the B-matrix D for T with the property that D is a diagonal matrix. A= [1 -2] Select one: O A. O B. O C. OD.For the given matrix and eigenvalue, find an eigenvector corresponding to the eigenvalue. A = {-24-5}, A = 6 150 31 Select one: [:1 H O C. [413' o D. [H