Unformatted text preview: subspace of U . 5. Let V be the vector space over the complex numbers of all functions from R into C , i.e., the space of all complex-valued functions on the real line. Let f 1 ( x ) = 1 ,f 2 ( x ) = e ix ,f 3 ( x ) = e-ix . Prove that f 1 ,f 2 ,f 3 are linearly independent. Let g 1 ( x ) = 1 ,g 2 ( x ) = cos x,g 3 ( x ) = sin x . Find an invertible 3 × 3 matrix P such that g j = 3 X i =1 P ij f i . 1...
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- Fall '08
- Vector Space, Intelligent Systems, hand compute, Intelligent Systems Fall