3 Given the matrix and its eigenvalues2 27 00 4 40 has eigenvalues R,2 and R,34 and R, = 00 3 30Find the new matrices (A, and Az and A3) for the matrix.0.27- 32 27 02 27Aand A,-and A, = 0 2 40- 30 404 40%3D3303 280 3-42 27 034 27 0O 27 0BA. =10 2 40and A20 34 40and A30 0 400 323 340 3272727C)0 - 30 40and A, = 0 - 30 40andA3- 30 403303030O 27 0- 32272 27 0(D)A,0 2 40and A2=and A, = 0 4 40-30 400 3 283-403 304 27 036 27 02 27 00 6 40and A2and A3EA, =0 38 400 4 40=0 3 323 640 3303.2.

Solution is written in below steps.

Answered: Given the matrix and its eigenvalues 2…

Given the matrix and its eigenvalues 2 27 0 0 4 40 has eigenvalues R, = 2 and R, = 34 and R, = 0 II 0 3 30 Find the new matrices (A, and Az and A3) for the matrix.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.4: Orthogonal Diagonalization Of Symmetric Matrices

Problem 16EQ

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Question

Given the matrix and its eigenvalues
2 27 0
0 4 40 has eigenvalues R,
2 and R,
34 and R, = 0
0 3 30
Find the new matrices (A, and Az and A3) for the matrix.
0.
27
- 32 27 0
2 27
A
and A,-
and A, = 0 2 40
- 30 40
4 40
%3D
3
30
3 28
0 3
-4
2 27 0
34 27 0
O 27 0
B
A. =
1
0 2 40
and A2
0 34 40
and A3
0 0 40
0 3
2
3 34
0 3
27
27
27
C)
0 - 30 40
and A, = 0 - 30 40
and
A3
- 30 40
3
30
30
30
O 27 0
- 32
27
2 27 0
(D)
A,
0 2 40
and A2=
and A, = 0 4 40
-30 40
0 3 28
3
-4
03 30
4 27 0
36 27 0
2 27 0
0 6 40
and A2
and A3
E
A, =
0 38 40
0 4 40
=
0 3 32
3 64
0 3
30
3.
2.

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