8/17/2019 LA_hw3 (2)

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APMAE 2101 Homework 9

1. For the points  yi   0 8 8 20

xi   0 1 4 4  find the coefficients of :

(a) (15 points) The closest line y   = ax  + b.

(b) (15 points) The closest parabola y   = ax2 + bx  + c.

2. (5 points) If  Q  has orthonormal columns what is the least-squares solution to  Qx  =  b?

3. Find an orthonormal basis using the Gram-Schmidt process for the columns of  A  and solve

Ax  = b  by least squares.

(a) (15 points)   A  =

1 1

2   −1

−2 4

b  =

1

2

7

.

(b) (15 points)   A  =

1   −2

1 0

1 1

1 3

and b  =

−4

−3

3

0

.

4. (40 points) From the book (4 points each):

8.4: 11, 12, 13, 14

8.5: 11, 12, 13, 14, 25, 26

Total points: 105