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Unformatted text preview: ( t ) = 1 + 2 t3 t 2 . (b) (6 points) Show that T is a linear transformation. (c) (6 points) Find the matrix of T relative to the standard bases of P 2 and P 3 . 7. Let W be the subspace of R 4 spanned by the orthogonal vectors 3 21 4 and 2 2 61 , and let y = 5 25 9 . (a) (10 points) Write y as the sum of a vector in W and a vector in W ⊥ . (b) (6 points) Find the distance from y to the subspace W . 8. (8 points) Find an orthogonal basis for the column space of A = 2 781 114 11 8 4 1 . 9. (8 points) Find a least squares solution of A x = b , where A = 1 2 231 3 and b = 3 1 2 ....
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 Fall '09
 KOCH
 Linear Algebra, M340L EXAM 3A

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