Cambridge Additional Mathematics

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Matrices (Chapter 12) 307

Amatrixis a rectangular array of numbers arranged inrowsandcolumns.

Each number within a matrix has a particular meaning.
You have been using matrices for many years without realising it. For example, a football premiership table
and a recipe can each be written as matrices.

Wo n Lost Drew Points
Manchester United 28 5 5 89
Manchester City 23 9 6 78
Chelsea 22 9 7 75
Arsenal
..
.

21 10 7 73

Ingredients Amount
sugar 1 tspn
flour 1 cup
milk 200 mL
salt 1 pinch

Consider these two items of information:

Shopping list
Bread 2 loaves
Juice 1 carton
Eggs 6
Cheese 1

Furniture inventory
chairs tables beds
Flat 6 1 2
Unit 9 2 3
House 10 3 4

We can write these tables as matrices by extracting the numbers and placing
them in round brackets:
number
B
J
E
C

0

B
@

2
1
6
1

1

C
A
and

CTB
F
U
H

0

@

612
923
10 3 4

1

A
or simply

0

B
@

2
1
6
1

1

C
A and

0

@

612
923
10 3 4

1

A

Notice how the organisation of the data is maintained in matrix form.
0
B
@

2
1
6
1

1
C
A

has 4 rows and 1 column, and we say that this
is a 4 £ 1 column matrixorcolumn vector.

column 2

row 3

0

@

612
923
10 3 4

1

A has^3 rows and^3 columns, and is called a
3 £ 3 square matrix.

this element is in row 3 , column 2
¡
30 ¡ 12

¢ has 1 row and 4 columns, and is called a
1 £ 4 row matrixorrow vector.

An m£n matrix hasmrows andncolumns.
m£n specifies theorderof a matrix.

A Matrix structure


Each number in a matrix
has a particular meaning.

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Y:\HAESE\CAM4037\CamAdd_12\307CamAdd_12.cdr Tuesday, 7 January 2014 6:00:29 PM BRIAN

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