Unformatted text preview: J of this matrix and write down cos( e A ) explicitly. 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. Problem 8. Consider the linear system ˙ x = Ax + w ( t ) where w ( t ) is a Tperiodic function, meaning that w ( T ) = w (0). There exists a Tperiodic solution to this system, meaning there exists an x (0) such that x ( t + T ) = x ( t ). Find this solution by ±rst determining x (0). 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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