solutions3bd

# solutions3bd - Math 33a/2, Quiz 3bd, November 1, 2007 Name:...

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Unformatted text preview: Math 33a/2, Quiz 3bd, November 1, 2007 Name: Suppose v1 = UCLA ID: 3 2 and v2 = . Note that {v1 , v2 } = B are a basis for R2 . Let 6 5 T : R2 R2 be the linear transformation such that T (v1 ) = v1 + v2 and T (v2 ) = 2v1 - 3v2 . 1. Compute the matrix of T with respect to the basis B. 2. Compute the standard matrix of T . 1 and 1 2 1 2 T (v2 ) B = . Hence the matrix B of T relative to the basis B is simply . -3 1 -3 5 -2 3 2 1 The change-of-basis matrix S is simply , and we compute S -1 = (3)(5)-(2)(6) -6 3 6 5 5 -2 1 = 3 . Hence the standard matrix A of T is given by -6 3 1 3 2 3 -6 1 2 A = SBS -1 = ( ) 6 5 1 -3 3 -2 5 1 5 0 3 -6 = ( ) 11 -3 3 -2 5 1 15 -30 = 3 39 -81 5 -10 = . 13 -27 Solution. Since T (v1 ) = v1 + v2 and T (v2 ) = 2v1 - 3v2 , we have T (v1 ) B = 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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