Problem 4.1-3a) Is the matrix A =2 0diagonalizable?1-3b) For which k is the matrix A= k 12 1-3 diagonalizable?2 1-3c) Find a 3 x 3 matrix A, which is not the identity or the zero matrix, such that A4 = A³.

As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Problem 4. 1 -3 a) Is the matrix A = 2 0 diagonalizable? 2 0 1 -3 b) For which k is the matrix A = k 12 1 -3 diagonalizable? 2 1 c) Find a 3 x 3 matrix A, which is not the identity or the zero matrix, such that A4 = A³.

Problem 4. 1 -3 a) Is the matrix A = 2 0 diagonalizable? 2 0 1 -3 b) For which k is the matrix A = k 12 1 -3 diagonalizable? 2 1 c) Find a 3 x 3 matrix A, which is not the identity or the zero matrix, such that A4 = A³.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.3: Matrix Algebra

Problem 78E

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Question

Problem 4.
1
-3
a) Is the matrix A =
2 0
diagonalizable?
1
-3
b) For which k is the matrix A
= k 12 1
-3 diagonalizable?
2 1
-3
c) Find a 3 x 3 matrix A, which is not the identity or the zero matrix, such that A4 = A³.

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