Early homework for Wednesday, September 4

If you submitted these by 5:00 pm Wednesday, you don't have to turn in 1.3, #13 and 12, 1.4 #8, 1.5 #15, or 1.7 #29 on Friday. These problems will deal with the following matrices:

1	5	0	5	0	-1
0	0	1	2	0	-2
0	0	0	0	1	1

1	0	4
0	-1	-3
0	0	-3

-3	-3	5
0	0	4
0	0	0

-2	-4	-3	-4
0	1	-2	0
0	0	2	1

and M=

1	4	-3	-3	-27
1	5	-1	-4	-22
-3	1	5	-4	26

Recall that we've seen M before. If you think they're relevant, you may cite earlier results about M without deriving them again.

Question 1:Give all solutions to the equation Ax=0, in parametric vector form.

Question 2:Which of the matrices A, B, C, D, and M above have columns that span all of R³? Justify your answer. (One sentence should suffice, at least if it's the right sentence.)

Question 3:Which of the matrices A, B, C, D, and M above have linearly independent columns? Justify your answer. (One sentence should again suffice.)