Early homework is due by 5:00 pm Wednesday.
If you did the early homework, you don't need to turn in problems
3, 13, or 21 from section 4.6, problem 15 from section 4.7, or problem 12 from section 4.9 on Friday. However, please make a note that you have done so.
Consider the matrices:
A=
1
5
0
5
0
-1
0
0
1
2
0
-2
0
0
0
0
1
1
,
B=
1
0
4
0
-1
-3
0
0
-3
,
C=
-3
-3
5
0
0
4
0
0
0
,
D=
-2
-4
-3
-4
0
1
-2
0
0
0
2
1
,
E=
2
-1
0
1
0
0
,
H=
1
5
-3
12
4
4
1
7
10
3
-1
5
-7
8
3
-2
4
-8
4
1
-2
2
-6
0
3
,
and J=
1
0
2
2
0
0
1
-1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
.
Recall that H is row-equivalent to J.
Question 1:
Find the rank of each matrix above. Question 2:
Find bases for the columnspace and rowspace of H.
Question 3:
Suppose that M and N are invertible n by n matrices. Let B1 be the basis for Rn consisting of the columns of M, and let B2 be the basis for Rn consisting of the columns of N. Find the change of basis matrix from B1 to B2. Justify your answer.
(Hint: consider the change of basis matrices to and from the standard basis.)