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Unformatted text preview: ~v = " 1 2 # is an eigenvector for a matrix A and that the corresponding eigenvalue is 2. Let B = A 43 A . Compute B~v . 9. Let A be the following matrix. Determine whether it is diagonalizable or not. If it is, ﬁnd an invertible S and a diagonal D such that D = S1 AS ; if it is not, explain why. (a) A = 1 1 1 1 1 1 1 1 1 (b) A = 1 1 1 0 1 0 0 1 0 10. Let A be a 2 × 2 matrix. Assume that " 1 1 # is an eigenvector of A with eigenvalue λ 1 =2 and that " 1 2 # is an eigenvector of A with eigenvalue λ 2 = 3. (a) Compute A ; (b) Find a closed formula for A n where n is a positive integer. 11. Let L : R 2 × 2→ R 2 × 2 be the linear transformation L ( A ) = A + A T , for any A ∈ R 2 × 2 . Find the eigenvalues and eigenmatrices of L . Is L diagonalizable?...
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This note was uploaded on 04/03/2008 for the course MATH 214 taught by Professor Conger during the Fall '08 term at University of Michigan.
 Fall '08
 Conger
 Linear Equations, Equations

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