Cambridge Additional Mathematics

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.

4037 Cambridge

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