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Unformatted text preview: = Z 2 2 f ( x ) g ( x )cos xdx denes an inner product on V . (b) Verify that < f,g > = Z 2 2 f ( x ) g ( x )sin xdx does not dene an inner product on V . 5. Let V = R [ x ], the real vector space of polynomials with real coecients. We dene < f,g > = R 11 f ( x ) g ( x ) dx , the standard inner product on this space. (a) Find a scalar a such that < a,a > = 1. (b) Find scalars b and c such that < a,b + cx > = 0 and < b + cx,b + cx > = 1. (c) Find scalars , and such that < a, + x + x 2 > = < b + cx, + x + x 2 > = 0 and < + x + x 2 , + x + x 2 > = 1 . 1...
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This note was uploaded on 04/29/2008 for the course PHYS 230 taught by Professor Harris during the Fall '07 term at McGill.
 Fall '07
 Harris

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