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Unformatted text preview: A-1 . 5. In each of the following, if possible, factor the matrix A into a product XDX-1 , where D is diagonal (a) A = • 4 2 3 3 ‚ (b) A = 1 0-1 3 3 2-2 (c) A = 2-2 3 3-2-1 2 2 6. For each of the matrices in Question 5, use the XDX-1 factorization to compute A 6 . 7. For each of the nonsingular matrices in Question 5, use use the XDX-1 factorization to compute A-1 8. In each of the following, if possible, orthogonally diagonalize each given matrix A , giving the diagonal matrix D and the diagonalizing orthogonal matrix P . (a) A = • 2 2 2 2 ‚ (b) A = -1-1-1-1-1-1 9. Show that if A is an n × n orthgonal matrix and x and y are vectors in R n , then ( A x ) · ( A y ) = x · y . 10. Show that if A is an orthogonal matrix, then A-1 is also orthogonal....
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