Given the following matrix: A = 1 -1 4 -1 2 0 1 3 -1 Complete the following: a) Its characteristic polynomial P(x)? b) An eigenvalue, other than 3, of matrix A corresponds to? c) The greatest algebraic multiplicity of the eigenvalues of matrix A corresponds to?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 28EQ
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Given the following matrix:
A =
1
-1
-1 2
0
1
4 3
-1
Complete the following:
a) Its characteristic polynomial PA(X)?
b) An eigenvalue, other than 3, of matrix A corresponds to?
c) The greatest algebraic multiplicity of the eigenvalues of matrix A corresponds to?
d) is the matrix A diagonalizable?
e) If 3 corresponds to an eigenvalue of matrix A, then the eigenspace associated with 3 is generated by?
Transcribed Image Text:Given the following matrix: A = 1 -1 -1 2 0 1 4 3 -1 Complete the following: a) Its characteristic polynomial PA(X)? b) An eigenvalue, other than 3, of matrix A corresponds to? c) The greatest algebraic multiplicity of the eigenvalues of matrix A corresponds to? d) is the matrix A diagonalizable? e) If 3 corresponds to an eigenvalue of matrix A, then the eigenspace associated with 3 is generated by?
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Hi, could you also help me with the answers for d) and e) ? thank you!

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