Question 2. Let 1 1 1 -1 A = -1 1 -1 -1 2 1 -1 1 -1 2 The eigenvalues of A are exactly 2± /3i. Show that A is diagonalizable over C and compute a diagonal matrix D and an invertible matrix V such that A = VDV-1.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 80E
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Q2. Math linear Algebra. Please explain step by step, clearly. Also, please do no take the answer from Chegg

Question 2. Let
2
1
1
1
1
-1
A
-1
1
1
-1
2
The eigenvalues of A are exactly 2 ± /3i. Show that A is diagonalizable over C and compute a diagonal
matrix D and an invertible matrix V such that A = V DV-1.
Transcribed Image Text:Question 2. Let 2 1 1 1 1 -1 A -1 1 1 -1 2 The eigenvalues of A are exactly 2 ± /3i. Show that A is diagonalizable over C and compute a diagonal matrix D and an invertible matrix V such that A = V DV-1.
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