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(2) Same problem with A 1 0 0 1 0 0 0 0 -2 0 1 -2 0 −1 -2 -2 - -

(2) Same problem with A 1 0 0 1 0 0 0 0 -2 0 1 -2 0 −1 -2 -2 - -

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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Problem No.2 plz! 

 

(1) Compute the rational canonical form for -1 −1 -1 -2 0 −1 6 3 4 A = That is, present it as SRS-¹, where R consists of companion ma- trix blocks along the diagonal and S is a change-of-basis matrix. Interpret the result in terms of a direct-sum decomposition of R³ under the action of the transformation T with matrix [T]ê = A. (2) Same problem with A = 1 0 A = 0 0 0 1 0 0 0 1 0 -1 -2 -2 -2 -2 and R4 instead of R³. [Note: from Exercise VI.B.2(a), you already know the normal form for AI4 – A.] (3) Once more, same problem with How does it depend on c? 1000 c100 0c10 00c1
Transcribed Image Text:(1) Compute the rational canonical form for -1 −1 -1 -2 0 −1 6 3 4 A = That is, present it as SRS-¹, where R consists of companion ma- trix blocks along the diagonal and S is a change-of-basis matrix. Interpret the result in terms of a direct-sum decomposition of R³ under the action of the transformation T with matrix [T]ê = A. (2) Same problem with A = 1 0 A = 0 0 0 1 0 0 0 1 0 -1 -2 -2 -2 -2 and R4 instead of R³. [Note: from Exercise VI.B.2(a), you already know the normal form for AI4 – A.] (3) Once more, same problem with How does it depend on c? 1000 c100 0c10 00c1
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