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Unformatted text preview: Math 33a/2, Quiz 3ac, October 30, 2007 Name: Suppose v1 = UCLA ID: 3 2 and v2 = . Note that {v1 , v2 } = B are a basis for R2 . Let 5 3 T : R2 R2 be the linear transformation such that T (v1 ) = 2v1 and T (v2 ) = v1  2v2 . 1. Compute the matrix of T with respect to the basis B. 2. Compute the standard matrix of T . 2 and 0 1 2 1 T (v2 ) B = . Hence the matrix B of T relative to the basis B is simply . 2 0 2 3 2 3 2 1 The changeofbasis matrix S is simply , and we compute S 1 = (3)(3)(2)(5) 5 3 5 3 3 2 = . Hence the standard matrix A of T is given by 5 3 Solution. Since T (v1 ) = 2v1 and T (v2 ) = v1  2v2 , we have T (v1 )
B = A = SBS 1 = = = 6 1 10 1 3 2 5 3 2 1 0 2 3 2 5 3 3 2 5 3 23 15 . 35 23 1 ...
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This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.
 Fall '08
 lee
 Math

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