Solve the following problems, showing any necessary work. Your answers must be exact, or must contain atleast four digits after the decimal point.

Note: Please handwrite it and make it clear>

MAT 242 Written Homework #6

1.A, 6.4, 6.A

Due: November 29

Solve the following problems, showing any necessary work. Your answers must be exact, or must contain at

least four digits after the decimal point.

−7

0

−1

−2 −5 1

1. Let W be the subspace spanned by

. Note that this basis is not orthogonal.

,

,

9

0

2

−12

10

4

5

0

a. [1 point] Find the orthogonal projection of into W.

10

15

b. [1 point] Find an orthogonal basis for W.

2. Find the best-fitting curve of each type below, using (−5, −214), (−1, −10), (0, −4), and (1, −4) for

data points.

a. [10 points] Lines: y = ax + b.

b. [10 points] Parabolas symmetric about the y-axis: y = ax2 + c.