B v is the space of dierentiable functions and w is

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Unformatted text preview: A. (b) V is the space of differentiable functions, and W is the set of those differentiable functions that satisfy f ￿ (3) = 0. 3. (a) Find a quadratic function of the form f (x) = c + dx2 that best fits the data (x, y ) = (−1, 1), (0, 1), (1, 2) in the least squares sense. (b) Verify that your function is a better fit than the constant function f (x) = 1. (c) How much better could you do if you considered instead functions of the form f (x) = c + bx + dx2 ? 4. Consider the subspace −1 −1 1 0 1 , 1 , 2 , 0 ⊆ R3 . V = span −1 1 0 −2 1 1. (a) Find the closest vector in V to the vector 1 (b) Find the matrix of the projection of R3 onto V . Hint: Depending on how you do this, your calculations could be much easier if you first choos...
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