solutions3ac

solutions3ac - Math 33a/2, Quiz 3ac, October 30, 2007 Name:...

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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 change-of-basis 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.

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