HW #10, due 3:50pm Friday, April 27

Note: Webwork sets for 6.4 and 6.5 are also due on April 27.

6.2 Orthogonal sets of vectors

4, 6 (Orthogonal set?)

20 (Normalize)

24 (True or False, and justify.)

35 (Show columns are orthogonal.) You may copy and paste this:

    [[-6,-3,6,1],
[-1,2,1,-6],
[3,6,3,-2],
[6,-3,6,-1],
[2,-1,2,3],
[-3,6,3,2],
[-2,-1,2,-3],
[1,2,1,6]]

Turn in a printout of your computation.

6.3 Orthogonal projections

2 (Orthogonal decomposition)

6 (Orthogonal projection on to plane.)

12 (Closest point in subspace.)

22 (True or false and justify.)

26 (Closest point in Col of matrix in 6.2.35.)

6.4 Gram-Schmidt process

See also Webwork assignment.

2 (GS for 2 vectors in R3.)

18 (True or false and justify.)

24 (Bigger GS exercise.)

25 (QR factorization using GS)

6.5 Least squares problems

Webwork assignment gives numerical examples.

18 (True or false and justify.)