(a) Given matrix A: (i) (ii) [0 0-3] A = 1 1 1 L20 5 Show with working that the eigenvalues of matrix A are 1, 2 and 3. Compute the eigenvectors of the corresponding eigenvalues. (iii) Hence obtain the eigendecomposition of A. ra CI

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 2
(a)
(b)
Given matrix A:
(i)
(ii)
(iii)
ГО 0
A = 1 1
-31
1
L2 0 5
Show with working that the eigenvalues of matrix A are 1, 2 and 3.
Compute the eigenvectors of the corresponding eigenvalues.
Hence obtain the eigendecomposition of A.
Prove that a 2x2 symmetric matrix B=
diagonalizable.
[with a, b, c ER is always
Transcribed Image Text:Question 2 (a) (b) Given matrix A: (i) (ii) (iii) ГО 0 A = 1 1 -31 1 L2 0 5 Show with working that the eigenvalues of matrix A are 1, 2 and 3. Compute the eigenvectors of the corresponding eigenvalues. Hence obtain the eigendecomposition of A. Prove that a 2x2 symmetric matrix B= diagonalizable. [with a, b, c ER is always
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