1 Let A = 0 3 4 -4. The eigenvalues of A are λ = -1 and λ = -2. (a) Find a basis for the eigenspace E-1 of A associated to the eigenvalue λ = -1 BE-1 -2 4 -2 0 (b) Find a basis of the eigenspace E-2 of A associated to the eigenvalue λ = -2. BE-27 40B Observe that the matrix A is diagonalizable.

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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1
Let A = 0
3
4 -4.
The eigenvalues of A are λ = -1 and λ = -2.
(a) Find a basis for the eigenspace E-1 of A associated to the eigenvalue
λ = -1
BE-1
-2
4
-2 0
(b) Find a basis of the eigenspace E-2 of A associated to the eigenvalue
λ = -2.
BE-2
409
Observe that the matrix A is diagonalizable.
Transcribed Image Text:1 Let A = 0 3 4 -4. The eigenvalues of A are λ = -1 and λ = -2. (a) Find a basis for the eigenspace E-1 of A associated to the eigenvalue λ = -1 BE-1 -2 4 -2 0 (b) Find a basis of the eigenspace E-2 of A associated to the eigenvalue λ = -2. BE-2 409 Observe that the matrix A is diagonalizable.
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