The matrix A = 1 3 3 -3 -5 -3 has eigenvalues X = 1 and X 3 3 1 Show that A is diagonalizable. = -2.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 7EQ
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this is one question with 2 part, after give answer plesae give a proof

1
3
-3 -5 -3 has eigenvalues
3
3
1
Show that A is diagonalizable.
The matrix A =
If TV → V is diagonalizable, show that V
=
1 and λ = -2.
Null T Range T.
Transcribed Image Text:1 3 -3 -5 -3 has eigenvalues 3 3 1 Show that A is diagonalizable. The matrix A = If TV → V is diagonalizable, show that V = 1 and λ = -2. Null T Range T.
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