are the same, i.e.
[bij]=[aij] if and only ifbij=aij
for every value ofiandj.
Weadd/subtractmatrices by adding/subtracting corresponding elements. So we can
only add or subtract matrices of the same size:
[aij]±[bij]=[aij±bij]
Generalising the idea of repeated addition we can definemultiplication of a matrix by a
scalar,k, according to:
k[aij]=[kaij]
i.e. we multiply each element by the scalark. This is just like multiplication by a scalar
in vector algebra.
Problem 13.3
Add all possible pairs of the following matrices:
A=
[
1 − 1
01
]
B=
[ 13 − 1
−10 2
21 0
]
C=
[
23
− 12
]
D=
[ 123
123
123
]
E=
[
2 − 1
10
]
Since only matrices of the same size can be added we can only addA,C,Etogether and
B,Dtogether. The possibilities are therefore
A+C=
[
1 − 1
01
]
+
[
23
− 12
]
=
[
1 + 2 − 1 + 3
0 − 11 + 2
]
=
[
32
− 13
]
CYE=
[
23
− 12
]
+
[
2 − 1
10
]
=
[
42
02
]
A+E=
[
1 − 1
01
]
+
[
2 − 1
10
]
=
[
3 − 2
11
]
B+D=
[ 13 − 1
−10 2
21 0
]
+
[ 123
123
123
]
=
[ 252
025
333
]