Find a family of the matrices that is similar to the matrix P=8 4 -3

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 64CR: a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving...
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(a) Find a family of the matrices that is similar to the matrix P=8
P
2
-
4
- 3
b)
Find eigenvalues and eigenvectors of the following matrix:
1 00
2 1 1
0 1 P
Determine (i) Eigenspace of each eigenvalue and basis of this
eigenspace (ii) Eigenbasis of the matrix
Is the matrix in part(b) is defective?
Transcribed Image Text:(a) Find a family of the matrices that is similar to the matrix P=8 P 2 - 4 - 3 b) Find eigenvalues and eigenvectors of the following matrix: 1 00 2 1 1 0 1 P Determine (i) Eigenspace of each eigenvalue and basis of this eigenspace (ii) Eigenbasis of the matrix Is the matrix in part(b) is defective?
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