Unformatted text preview: V to W , and let T be a subspace of W . Then { v ∈ V  L ( v ) ∈ T } is a subspace of V . True. Verify directly from deﬁnitions of subspace and linear transformation. 4. Let E = 1 1 , 1 2 1 , 1 1 1 and F = ±² 1 1 ³ , ² 2 1 ³´ . Let L ( x ) be a linear transformation from R 3 to R 2 deﬁned by L ( x ) = ² x 3 x 1 ³ . Find the matrix representing L with respect to the ordered bases E and F . See supplement for Chap 4 for the situating when you are ONLY given the matrix representation of L in standard bases. Here L is explicitly given, so one just computes L 1 1 = ² 1 1 ³ , then expand ² 1 1 ³ in terms of the basis F . This gives the ﬁrst column of the matrix A = L E,F . One then proceed with L 1 2 1 and L 1 1 1 ....
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This note was uploaded on 04/18/2010 for the course FINANCE 1231854365 taught by Professor Wuyiling during the Spring '10 term at Nashville State Community College.
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