Unformatted text preview: 1 2 3 3 = 2 1 2 3 3 . Show that A is unique. (b) If A is the matrix in (a), ﬁnd the eigenvalues of A and a basis for each eigenspace of A . 4. (a) Find a 4 × 4 real matrix A whose null space and column space are spanned by the column matrices 1 2 3 4 , 4 3 2 1 . (b) What are the eigenvalues of the matrix A found in (a)? Does R 4 × 1 have a basis consisting of eigenvectors of A ? 5. Let A = 1 2 2 2 2 1 2 2212221 . (a) Using the fact that A 2 = I , ﬁnd the eigenvalues of A and a basis for each eigenspace of A . (b) Find an invertible matrix P such that P1 AP is a diagonal matrix....
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 Winter '06
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 Linear Algebra, Algebra, Matrices, real matrix, McGill University Math

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