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Mathematics
Mathematics
Problem
The matrices
A
=
[
1
2
3
4
]
A=\begin{bmatrix}1&2\\3&4\end{bmatrix}
A
=
[
1
3
2
4
]
,
B
=
[
2
−
1
0
5
]
B=\begin{bmatrix}2&-1\\0&5\end{bmatrix}
B
=
[
2
0
−
1
5
]
and
C
=
[
1
0
2
1
]
C=\begin{bmatrix}1&0\\2&1\end{bmatrix}
C
=
[
1
2
0
1
]
are given. a. (i) Find
(
A
+
B
)
C
(A+B)C
(
A
+
B
)
C
. b. (ii) Find
A
C
AC
A
C
and
B
C
BC
B
C
, and hence
A
C
+
B
C
AC+BC
A
C
+
B
C
. c. (iii) Show that the results obtained in parts (i) and (ii) are equal.
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