Let At be a matrix that depends on r and is given by 4-[30] At = t (a) For which te R matrix At has no real eigenvalues for At? (b) For which t € R matrix At has exactly one real distinct eigenvalue? Give that eigenvalue. (c) For which tER matrix At has two different real eigenvalues? Give one such eigenvalue as a function of t.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4. Let At be a matrix that depends on r and is given by
At
t
3
-2 1
(a) For which te R matrix At has no real eigenvalues for At?
(b) For which t E R matrix At has exactly one real distinct eigenvalue? Give that eigenvalue.
(c) For which te R matrix At has two different real eigenvalues? Give one such eigenvalue
as a function of t.
Transcribed Image Text:4. Let At be a matrix that depends on r and is given by At t 3 -2 1 (a) For which te R matrix At has no real eigenvalues for At? (b) For which t E R matrix At has exactly one real distinct eigenvalue? Give that eigenvalue. (c) For which te R matrix At has two different real eigenvalues? Give one such eigenvalue as a function of t.
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