[o Let A be a 3 x 3 diagonalizable matrix, P = 1 -1 Lo [2 0 P-1 =| 3 0 -2|,D = |0 0 lo o 1 1 -3 0 3 -1. If P¯ª A P = D then A³ 16 [2 0 -2 8. 3 8. 26 18 [3 0 -3] Lo -27 -19. is equal to the above matrix is equal to the above matrix 8 0 -8 8 [27 _0 0 -27] O is equal to the above matrix None of these NIM

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 72E: Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.
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Question
3
Let A be a 3 x 3 diagonalizable matrix, P = |1 -1
3
Lo
1
1
[2 0 0
P-1 =| 3 0 -2|, D = |0 0
lo o
1
1
l-3 0
3
If P-1 AP = D then A3
16
8.
[2 0
6 8
-3
-21
3
26
18
L3 _ 0
Lo
-27 -19]
is equal to the above matrix
is equal to the above matrix
8.
-8
8
8
[27 _0 -27.
is equal to the above matrix
None of these
Transcribed Image Text:3 Let A be a 3 x 3 diagonalizable matrix, P = |1 -1 3 Lo 1 1 [2 0 0 P-1 =| 3 0 -2|, D = |0 0 lo o 1 1 l-3 0 3 If P-1 AP = D then A3 16 8. [2 0 6 8 -3 -21 3 26 18 L3 _ 0 Lo -27 -19] is equal to the above matrix is equal to the above matrix 8. -8 8 8 [27 _0 -27. is equal to the above matrix None of these
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