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Mathematics
Mathematics
Problem
Let
k
=
3
k=3
k
=
3
,
A
=
[
1
0
2
−
1
3
1
]
A=\begin{bmatrix}1&0&2\\-1&3&1\end{bmatrix}
A
=
[
1
−
1
0
3
2
1
]
and
B
=
[
2
1
0
−
1
1
4
]
B=\begin{bmatrix}2&1\\0&-1\\1&4\end{bmatrix}
B
=
2
0
1
1
−
1
4
. a. (i) Compute
A
B
AB
A
B
. b. (ii) Compute
k
(
A
B
)
k(AB)
k
(
A
B
)
. c. (iii) Compute
(
k
A
)
B
(kA)B
(
k
A
)
B
. d. (iv) Compute
A
(
k
B
)
A(kB)
A
(
k
B
)
. e. (v) Verify that
k
(
A
B
)
=
(
k
A
)
B
=
A
(
k
B
)
k(AB)=(kA)B=A(kB)
k
(
A
B
)
=
(
k
A
)
B
=
A
(
k
B
)
.
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