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- V = span(S), where S = {(1, i, 0), (1 - i, 2, 4i)}, and x = (3 + i, 4i, -4)
- (1)Apply the Gram Schmidt process to the given subset S of
- the inner product space V to obtain an orthogonal basis for span(S).
- (2)Normalize the vectors in this basis to obtain an orthonormal basis B for span(S).
- (3)Compute the Fourier coefficients of the given vector relative to 0 by solving the
- system of equations a1u1 + a2u2 + a3u3 = x, where u123 are the vectors of basis B
- (4)Compute the Fourier coefficients directly by ai = <x, ui>
- B = { (1/(2^.5))(1, i, 0), (1/(2(17^.5)))(1 + i, 1 - i, 4i)}
- (7 + i)/(2^.5) , (17^.5)i
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