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(a) With the aid of software, find the eigenvalues of B and their algebraic and geometric multiplicities. (b) Use Theorem DMFE on page 410 of Beezer to prove that B is not diagonalizable.

(a) With the aid of software, find the eigenvalues of B and their algebraic and geometric multiplicities. (b) Use Theorem DMFE on page 410 of Beezer to prove that B is not diagonalizable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Theorem DMFE Diagonalizable Matrices have Full Eigenspaces Suppose A is a square matrix. Then A is diagonalizable if and only if 7a (A) = as (A) for every eigenvalue ) of A.
Transcribed Image Text:Theorem DMFE Diagonalizable Matrices have Full Eigenspaces Suppose A is a square matrix. Then A is diagonalizable if and only if 7a (A) = as (A) for every eigenvalue ) of A.
1 -2 2 2 1 -2 2 1 2 -2 2 1 0 1 -1 Let B = -1 -1 0 2 1 -1 0 0 0 (a) With the aid of software, find the eigenvalues of B and their algebraic and geometric multiplicities. (b) Use Theorem DMFE on page 410 of Beezer to prove that B is not diagonalizable. 2.
Transcribed Image Text:1 -2 2 2 1 -2 2 1 2 -2 2 1 0 1 -1 Let B = -1 -1 0 2 1 -1 0 0 0 (a) With the aid of software, find the eigenvalues of B and their algebraic and geometric multiplicities. (b) Use Theorem DMFE on page 410 of Beezer to prove that B is not diagonalizable. 2.
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