Let A=[-2 2 2; 2 1 4; 2 4 1] and v1=[2 1 -2] a. show that v1 is an eigenvector of A. What is the eigenvalue? b. Find a basis for the λ-eigenspace, where λ is the eigenvalue of v1. What is the algebraic multiplicity of λ? c. Use the trace and /or determinant properties of eigenvalues, trace(A) = λ1+λ2+....+λn, det A=λ1λ2..,...λn to determine the remaining eigenvalues(s) of A.
Let A=[-2 2 2; 2 1 4; 2 4 1] and v1=[2 1 -2] a. show that v1 is an eigenvector of A. What is the eigenvalue? b. Find a basis for the λ-eigenspace, where λ is the eigenvalue of v1. What is the algebraic multiplicity of λ? c. Use the trace and /or determinant properties of eigenvalues, trace(A) = λ1+λ2+....+λn, det A=λ1λ2..,...λn to determine the remaining eigenvalues(s) of A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let A=[-2 2 2; 2 1 4; 2 4 1] and v1=[2 1 -2]
a. show that v1 is an eigenvector of A. What is the eigenvalue?
b. Find a basis for the λ-eigenspace, where λ is the eigenvalue of v1. What is the algebraic multiplicity of λ?
c. Use the trace and /or determinant properties of eigenvalues,
trace(A) = λ1+λ2+....+λn, det A=λ1λ2..,...λn
to determine the remaining eigenvalues(s) of A.
d. Find an orthogonal matrix P and a diagonal matrix D diagonalising A
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