h6 - L and (2 ,-1) is perpendicular to L .) (b) Use part...

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Homework Set 6 for MAS 4105 Due Friday, February 24 1. Let T : V W be a linear transformation which is one-to-one, and let { vx 1 , . . .,vx n } be a linearly independent subset of V . Prove that { T ( vx 1 ) , . . ., T ( vx n ) } is a linearly independent subset of W . 2. Let L be the line in R 2 with equation x 2 = 2 x 1 . Let T : R 2 R 2 be the linear transformation which maps vx R 2 to its reFection through L . (a) Compute T (1 , 2) and T (2 , - 1). (Note that (1 , 2) is parallel to
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Unformatted text preview: L and (2 ,-1) is perpendicular to L .) (b) Use part (a) to compute T (1 , 0) and T (0 , 1). (c) ind [ T ] , where = { (1 , 0) , (0 , 1) } . (d) Use part (c) to compute T (7 , 5). The following problems are strongly recommended, but should not be turned in: 2.3: 1, 2, 3, 4, 8, 10, 11, 12 2.4: 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 14, 16, 17, 18...
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