Unformatted text preview: (b) What are the eigenvalues of e At ? (c) Suppose this matrix A were the dynamic matrix of an LTI system. What happens to the state trajectory over time (magnitude grows, decays, remains bounded. ..)? Problem 4. You are told that A : R n → R n and that R ( A ) ⊂ N ( A ). Can you determine A up to a change of basis? Why or why not? Problem 6. Let A ∈ R n × n be nonsingular. True or false: the nullspace of cos ( log ( A )) is an Ainvariant subspace? Problem 7. Consider A ∈ R n × n , b ∈ R n . Show that span { b, Ab, . . . , A n1 b } is an Ainvariant subspace. 1...
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This note was uploaded on 12/09/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at Berkeley.
 Fall '10
 ClaireTomlin
 Electrical Engineering

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