h5 - T ] C B of T with respect to the basis B = { x,x + x 2...

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Homework Set 5 for MAS 4105 Due Friday, February 17 1. Let T : V W be a linear transformation and let 1 ,...,v± n be vec- tors in V such that T ( 1 ) ,...,T ( n ) are distinct linearly independent vectors in W . Prove that 1 ,...,v± n are linearly independent in V . 2. DeFne T : P 2 ( R ) P 2 ( R ) by setting T ( f ) = ( X + 2) f ( X ). ±ind bases for N ( T ) and R ( T ). (You may assume that T is a linear transformation.) 3. DeFne T : P 2 ( R ) R 2 by setting T ( f ) = ( f (3) ,f ( 1)). ±ind the matrix [
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Unformatted text preview: T ] C B of T with respect to the basis B = { x,x + x 2 , 2 + x } for P 2 ( R ) and the basis C = { (1 , 2) , (2 , 3) } for R 2 . (You may assume that T is a linear transformation, and that B and C are bases.) The following problems are strongly recommended, but should not be turned in: 2.2: 1, 2acdfg, 3, 4, 5, 6, 7, 8 2.3: 1, 2, 3, 4, 8, 10, 11, 12...
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