Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 13, x1 = (1, 2, –1) 12 = -3, x2 = (-2, 1 0) 23 = -3, x3 = (3, 0, 1) -1 4 -6 %3! A = 5 -12 -2 -4 3 -1 4 -6 1 Ax1 4 5 -12 = 13 2 = 11x1 -2 -4 3 -1 -1 -1 4 -6 -2 -2 Ax2 4 5 -12 = 12x2 = -2 -4 3 -1 4 -6 Ахз 4 5 -12 -3 0 23X3 %3D -2 -4 3

Linear Algebra: A Modern Introduction
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Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
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7.
DETAILS
LARLINALG8 7.1.004.
Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector.
11 = 13, x1 = (1, 2, –1)
12 = -3, x2 = (-2, 1 0)
23 = -3, x3 = (3, 0, 1)
-1
4
-6
A =
4
5 -12 ,
-2 -4
-1
4
-6
1
1
Ax1
4
5 -12
= 13
= 11x1
%3D
-2 -4
3
-1
-1
4
-6
-2
-2
Ax2 =
4
5 -12
1
-3
= 12x2
-2 -4
3
-1
4
-6
3
Ахз
5 -12
-3 0
= 13x3
%3D
-2 -4
3
Transcribed Image Text:7. DETAILS LARLINALG8 7.1.004. Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 13, x1 = (1, 2, –1) 12 = -3, x2 = (-2, 1 0) 23 = -3, x3 = (3, 0, 1) -1 4 -6 A = 4 5 -12 , -2 -4 -1 4 -6 1 1 Ax1 4 5 -12 = 13 = 11x1 %3D -2 -4 3 -1 -1 4 -6 -2 -2 Ax2 = 4 5 -12 1 -3 = 12x2 -2 -4 3 -1 4 -6 3 Ахз 5 -12 -3 0 = 13x3 %3D -2 -4 3
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