must be properly included. The elements can be complex numbers. What we want to do
is construct an ‘algebra’ for such arrays that enables us to treatAandbas much as
possible like ordinary algebraic objects. The system of equation (13.1) already suggests
some ideas here.
We put the quantitiesx,yin a 2×1 matrix of their own:
u=[
x
y]and write (13.1) as
[
21
1 − 2][
x
y]
=[
3
− 1]or
Au=b
If this is to be a symbolic shorthand for (13.1) then this essentially defines the ‘product’
Auof the two matricesAandu. Have a go at determining the rule for multiplying matrices
yourself. The formal definition is given in Section 13.3
Problem 13.1
Write the system of equationsaY 3 b= 1
2 aYb= 0in matrix formAu=b.The arrays are:
A=[
13
21]
b=[
1
0]
u=[
a
b]so the equations become
[
13
21][
a
b]
=[
1
0]Problem 13.2
‘Multiply’ the following matrix products(i)[
− 10
12][
x
y]
(ii)[
23
41][
2
1](iii)[
3 − 1
42][
12
− 11]