This preview shows page 1. Sign up to view the full content.
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...
View Full
Document
 Fall '05
 HUI
 Math, Linear Algebra, Algebra

Click to edit the document details