Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 %3D 13, х1 %3 (1, 2, —1) 12 = -3, x2 = (-2, 1 0) Аз %3D —3, Xз %3D (3, 0, 1) -1 4 -6 A = 4 5 -12 -2 -4 3 -- I -1 4 -6 1 Ах1 4 -12 2 13 2 -2 -4 3 -1 -1 -1 4 -6 -2 -2 Ax2 4 5 -12 1 -3 1 12x2 -2 -4 3 -1 4 -6 Axa 12 3

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 1BEXP
Question
Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector.
11 %3D 13, х1 %3 (1, 2, —1)
12 = -3, x2 = (-2, 1 0)
Аз %3D —3, Xз %3D (3, 0, 1)
-1
4
-6
А —
4
5 -12
-2 -4
3
I
-1
4
-6
1
Ах1
4
-12
2
13
2
-2 -4
3
-1
-1
-1
4
-6
-2
-2
Ax2
4
5 -12
1
-3
1
12x2
-2 -4
3
--
-1
4
-6
3
Ax3
4
5 -12
-3
13x3
-2
-4
3
1
1
Transcribed Image Text:Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 %3D 13, х1 %3 (1, 2, —1) 12 = -3, x2 = (-2, 1 0) Аз %3D —3, Xз %3D (3, 0, 1) -1 4 -6 А — 4 5 -12 -2 -4 3 I -1 4 -6 1 Ах1 4 -12 2 13 2 -2 -4 3 -1 -1 -1 4 -6 -2 -2 Ax2 4 5 -12 1 -3 1 12x2 -2 -4 3 -- -1 4 -6 3 Ax3 4 5 -12 -3 13x3 -2 -4 3 1 1
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