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How many eigenvalues of A are controllable?

How many eigenvalues of A are controllable?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve Q5 only
SOLVE Q5 ONLY Consider the state matrix A and input matrix B given by -1 1 1 A = 1 -2 1 ;B= 1 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]T. Then T is given by 4) The matrices A = T AT-l and B=TB is given by 5) How many eigenvalues of A are controllable?
Transcribed Image Text:SOLVE Q5 ONLY Consider the state matrix A and input matrix B given by -1 1 1 A = 1 -2 1 ;B= 1 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]T. Then T is given by 4) The matrices A = T AT-l and B=TB is given by 5) How many eigenvalues of A are controllable?
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