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(c) Find the characteristic polynomial PA(t) of the matrix A given below, and then the eigen- values of A. -1 -1 0 2 A 2 1 -1 (d) Choose one of the eigenvalues of A you found in (c), and find an eigenvector of A corre- sponding to this eigenvalue.

(c) Find the characteristic polynomial PA(t) of the matrix A given below, and then the eigen- values of A. -1 -1 0 2 A 2 1 -1 (d) Choose one of the eigenvalues of A you found in (c), and find an eigenvector of A corre- sponding to this eigenvalue.

Linear Algebra: A Modern Introduction
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 29EQ
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4. Let V be a vector space over C and let L: V →V be a linear transformation. (a) State the definition of an eigenvector of L. (b) Let A e C be arbitrary. State the definition of V, the A-eigenspace of L, and prove that it is a subspace of V. (c) Find the characteristic polynomial PA(t) of the matrix A given below, and then the eigen- values of A. -1 -1 2 A : 2 1 -1 (d) Choose one of the eigenvalues of A you found in (c), and find an eigenvector of A corre- sponding to this eigenvalue.
Transcribed Image Text:4. Let V be a vector space over C and let L: V →V be a linear transformation. (a) State the definition of an eigenvector of L. (b) Let A e C be arbitrary. State the definition of V, the A-eigenspace of L, and prove that it is a subspace of V. (c) Find the characteristic polynomial PA(t) of the matrix A given below, and then the eigen- values of A. -1 -1 2 A : 2 1 -1 (d) Choose one of the eigenvalues of A you found in (c), and find an eigenvector of A corre- sponding to this eigenvalue.
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