are the same, i.e.
[bij]=[aij] if and only ifbij=aijfor 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]