Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 1, = 4, x, = (1, 0, 0) , 12 = 2, x, = (1, 2, 0) А3%3D 3, х3 3D (-4, 1, 1) 4 -1 5 %3D A = 2 1 0 3 4 -1 5 Ax, = 2 1 = 4 0 = 0 3 4 -1 5 1 Ax2 = 2 1 = 2 2 = 12x2 0 3 4 -1 5 -4 4 Ax3 1= 13x3 2 1 = 3 0 3 1 1
Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 1, = 4, x, = (1, 0, 0) , 12 = 2, x, = (1, 2, 0) А3%3D 3, х3 3D (-4, 1, 1) 4 -1 5 %3D A = 2 1 0 3 4 -1 5 Ax, = 2 1 = 4 0 = 0 3 4 -1 5 1 Ax2 = 2 1 = 2 2 = 12x2 0 3 4 -1 5 -4 4 Ax3 1= 13x3 2 1 = 3 0 3 1 1
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector.
[ 4 -1 5] 1, = 4, x, = (1, 0, 0)
| 12 = 2, x, = (1, 2, 0)
I 13 = 3, x3 = (-4, 1, 1)
A =
2 1
%3D
0 3
4 -1 5
Ax, =
2 1
= 4 0
%3D
0 3
4 -1 5
1
Ax2 =
= 2 2
= 1,x2
2 1
2
%3D
0 3
4 -1 5
-4
-4
Ax3 =
1 = 13x3
2 1
1
: 3
=
%3D
0 3
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F83a8be48-ff82-415f-b202-4e48f43fd534%2Fe9bfe527-bf1a-4acd-8479-7fdea808eae6%2Fnd1623_processed.png&w=3840&q=75)
Transcribed Image Text:Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector.
[ 4 -1 5] 1, = 4, x, = (1, 0, 0)
| 12 = 2, x, = (1, 2, 0)
I 13 = 3, x3 = (-4, 1, 1)
A =
2 1
%3D
0 3
4 -1 5
Ax, =
2 1
= 4 0
%3D
0 3
4 -1 5
1
Ax2 =
= 2 2
= 1,x2
2 1
2
%3D
0 3
4 -1 5
-4
-4
Ax3 =
1 = 13x3
2 1
1
: 3
=
%3D
0 3
1
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