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1) Let A(x) = -1 0 1 0 -2 -2 -1 x 0 xER. (i) For what values of x is A(z) diagonalizable? Give a reason for your answer. (ii) For those values of x obtained in your answer to part (i), find an invertible matrix P(x) which diagonalizes A(x), i.e. (P(x))¹ A(x) P(x) = D(x),

1) Let A(x) = -1 0 1 0 -2 -2 -1 x 0 xER. (i) For what values of x is A(z) diagonalizable? Give a reason for your answer. (ii) For those values of x obtained in your answer to part (i), find an invertible matrix P(x) which diagonalizes A(x), i.e. (P(x))¹ A(x) P(x) = D(x),

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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(1) Let A(x) = 9). X 0 -2 -2 -1 -1 0 1 where D(x) is a diagonal matrix. x ER. (i) For what values of x is A(x) diagonalizable? Give a reason for your answer. (ii) For those values of r obtained in your answer to part (i), find an invertible matrix P(x) which diagonalizes A(x), i.e. (P(x))¹ A(x) P(x) = D(x),
Transcribed Image Text:(1) Let A(x) = 9). X 0 -2 -2 -1 -1 0 1 where D(x) is a diagonal matrix. x ER. (i) For what values of x is A(x) diagonalizable? Give a reason for your answer. (ii) For those values of r obtained in your answer to part (i), find an invertible matrix P(x) which diagonalizes A(x), i.e. (P(x))¹ A(x) P(x) = D(x),
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