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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
0 1 , 1 , 2 , 0 ⊆ R3 .
V = span −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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