4) The matrices à = T AT-1 and B=TB is given by 1 1 0 à = -1 1 B : 1 1 1 -2 1 2. 1 1 1 -1 0 1 -2 0 0 1 1 -1 1 0 1 -2 1 0 0 1 1 1 à = 0 -1 ;B= 1 1 -2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 10AEXP
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Question
Solve Q4 only
SOLVE Q4 ONLY
Consider the state matrix A and input matrix B given by
-1
1
1
A =
1
-2
1
;B=
1
1
1
2
3) Choose a similarity transformation matrix T such that T-1 is formed by taking the first two linearly independent columns of C and the last vector
as [0 0 1]". Then T is given by
4) The matrices À = T AT-1 and B= TB is given by
1
1
Ã
-1
1
0;B=
1
1
1
-2
1.
[1
1
1
A =
-1
;B =
0 1
-2
1
A =
-1
1
0;B=
1
1
-2
1
1
1
A =
-1
;B= |1
1
-2
[1
2.
Transcribed Image Text:SOLVE Q4 ONLY Consider the state matrix A and input matrix B given by -1 1 1 A = 1 -2 1 ;B= 1 1 1 2 3) Choose a similarity transformation matrix T such that T-1 is formed by taking the first two linearly independent columns of C and the last vector as [0 0 1]". Then T is given by 4) The matrices À = T AT-1 and B= TB is given by 1 1 Ã -1 1 0;B= 1 1 1 -2 1. [1 1 1 A = -1 ;B = 0 1 -2 1 A = -1 1 0;B= 1 1 -2 1 1 1 A = -1 ;B= |1 1 -2 [1 2.
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