Given that A is a 3 × 3 matrix with eigen pairs (-9, 3 (12, -2). Find the matrix B = M-¹AM where M = b11 b12 b13 Let B = b21 b22 b23 then b31 b32 b33 b11 = , b13 b21 = b31 || 1,612 , b22 2 " = || = b32 = " -2), (1, = 1, 623 b33 || = 4 -0.[3 4 3 1 3 -2 -2 1 5 || and

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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1
Given that A is a 3 x 3 matrix with eigen pairs (-9, -2
5
3
(12, -2). Find the matrix B = M-¹AM where M
=
b₁1
b12 b13
. Let B =
b22 b23
then
b32 b33
b11
=
, b13
=
b21
b31
||
b21
b31
, b12
,
"
=
b22
=
b32 =
=
, b23 =
, b33
(1,
4
3
-1
4
3 and
-1
3
1
-2 -2
1
5
Transcribed Image Text:1 Given that A is a 3 x 3 matrix with eigen pairs (-9, -2 5 3 (12, -2). Find the matrix B = M-¹AM where M = b₁1 b12 b13 . Let B = b22 b23 then b32 b33 b11 = , b13 = b21 b31 || b21 b31 , b12 , " = b22 = b32 = = , b23 = , b33 (1, 4 3 -1 4 3 and -1 3 1 -2 -2 1 5
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