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3. Find all the possible pairs of matrices that can be legally multiplied, and
give the dimensions of the resulting product. Include “pairs” in which a
matrix is multiplied by itself. (Hint: there are 14 pairs.)
4. Compute the following matrix products. If the product is not possible, just
say so.
1 −2
5
−3
7
(a)
0
4
1/3
6
−7
(b)
3
3
−4
5
2
4
−2
3
5
0
3
(c)
3 −1
4
5
7
−6
1
−4
2
2
4
1
3
5
0
0
0
0
1
0
0
(d)
x
y
z
w
0
0
1
0
0
0
0
1
−5
1
(e)
7 −2
7
3
1
0
m
11
m
12
(f)
0
1
m
21
m
22
6
−7
(g)
3
3
−4
5
2
3
a
11
a
12
a
13
b
11
b
12
b
13
4
5
(h)
a
21
a
22
a
23
b
21
b
22
b
23
a
31
a
32
a
33
5. For each of the following matrices, multiply on the left by the row vector
[5,−1, 2]. Then consider whether multiplication on the right by the column
vector [5,−1, 2]
T
will give the same or a different result. Finally, perform
this multiplication to confirm or correct your expectation.
2
4
3
5
1
0
0
(a)
0
1
0
0
0
1
2
4
3
5
2
5
−3
(b)
1
7
1
−2 −1
4
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