The following problem is about a 4 x 4 matrix A, (a) (b) (c) (d) true. A = 2 -3 0 4 0 1-2 4 24-1-2 0 2 -2 3 Find the eigenvalues of matrix A using Gauss Elimination. Find all the eigenvectors for each eigenvalues found above. Determine the algebraic multiplicity and geometric multiplicity of each eigenvalues. For each eigenvalue and corresponding eigenvector, show that, Ax= Ax is hold

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 26EQ
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The following problem is about a 4 x 4 matrix A,
-3 0
4
2
1 -2
4 -1 -2
0 2 -2
4
A =
3
(a)
Find the eigenvalues of matrix A using Gauss Elimination.
(b)
Find all the eigenvectors for each eigenvalues found above.
(c)
Determine the algebraic multiplicity and geometric multiplicity of each eigenvalues.
(d)
For each eigenvalue and corresponding eigenvector, show that, Ax = dx is hold
truc.
||
Transcribed Image Text:The following problem is about a 4 x 4 matrix A, -3 0 4 2 1 -2 4 -1 -2 0 2 -2 4 A = 3 (a) Find the eigenvalues of matrix A using Gauss Elimination. (b) Find all the eigenvectors for each eigenvalues found above. (c) Determine the algebraic multiplicity and geometric multiplicity of each eigenvalues. (d) For each eigenvalue and corresponding eigenvector, show that, Ax = dx is hold truc. ||
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