solutions3ac - Math 33a/2 Quiz 3ac Name Suppose v1 = UCLA...

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Math 33a/2, Quiz 3ac, October 30, 2007 Name: UCLA ID: Suppose v 1 = 3 5 and v 2 = 2 3 . Note that { v 1 , v 2 } = B are a basis for R 2 . Let T : R 2 R 2 be the linear transformation such that T ( v 1 ) = 2 v 1 and T ( v 2 ) = v 1 - 2 v 2 . 1. Compute the matrix of T with respect to the basis B . 2. Compute the standard matrix of T . Solution. Since T ( v 1 ) = 2 v 1 and T ( v 2 ) = v 1 - 2 v 2 , we have ( T ( v 1 ) ) B = 2 0 and ( T ( v 2 ) ) B = 1 - 2 . Hence the matrix B of T relative to the basis
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