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Unformatted text preview: show a nontrivial linear combination resulting in the zero function. 3. (50 points) Solve the initial value problem x pp ( t ) + 2 x p ( t )3 x ( t ) = cos t, x (0) = 0 , x p (0) = 0 . (Note that this is not an equation of a damped vibration as the spring force term has a negative coeFcient.) 4. Let A : = 1 1 1 1 1 1 1 1 1 . (a) (20 points) Determine the eigenvalues of this matrix. (b) (20 points) Show bases for each eigenspace corresponding to the eigenvalues....
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 Fall '05
 BALAZS
 Linear Algebra, Combinatorics, Matrices, Vector Space, Sets, linearly independent functions, nontrivial linear combination, zero function

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