Verify that 1; is an eigenvalue of A and that x, is a corresponding eigenvector. A13 13, х, 3 12 = -3, x2 = (-2, 1 0) 13 = 1 4 -6 (1, 2, –1) = A = 4 5 -12 -2 -4 3 -3, хз — (3, 0, 1) -1 4 -6 1 Ax1 = 13 2 =1,x1 4 5 -12 2 = -2 -4 -1 -1 -1 4 -6 -2 -2 Ax2 = = -3 1 = 12x2 4 5 -12 1 -2 -4 1 4 -6 3 Ax3 4 5 -12 -3 0 = 13x3 = -2 -4 3 1

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Verify that 1; is an eigenvalue of A and that x, is a corresponding eigenvector.
-1
4
-6
13, х, —
(1, 2, –1)
11
-3, х, 3D
-3, хз — (3, 0, 1)
=
A =
4
5 -12
(-2, 1 0)
-2 -4
3
1
4
-6
1
1
Ax1
= 13
2 =1,x1
4
5 -12
=
-2 -4
3
-1
-1
1
4
-6
-2
-2
Ax2 =
= -3
1 = 12x2
4
5 -12
1
=
%3D
-2 -4
3
1
4
-6
3
Ax3 =
5 -12
-3 0
= 13x3
4
-2 -4
3
1
1
Transcribed Image Text:Verify that 1; is an eigenvalue of A and that x, is a corresponding eigenvector. -1 4 -6 13, х, — (1, 2, –1) 11 -3, х, 3D -3, хз — (3, 0, 1) = A = 4 5 -12 (-2, 1 0) -2 -4 3 1 4 -6 1 1 Ax1 = 13 2 =1,x1 4 5 -12 = -2 -4 3 -1 -1 1 4 -6 -2 -2 Ax2 = = -3 1 = 12x2 4 5 -12 1 = %3D -2 -4 3 1 4 -6 3 Ax3 = 5 -12 -3 0 = 13x3 4 -2 -4 3 1 1
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