Cambridge Additional Mathematics

Matrices (Chapter 12) 313

EXERCISE 12B.2

1 If B=

μ

612

24 6

¶

, find:

a 2 B b^13 B c 121 B d ¡^12 B

2 If A=

μ

235

164

¶

and B=

μ

121

123

¶

, find:

a A+B b A¡B c 2 A+B d 3 A¡B

3 A builder builds a block of 12 identical flats. Each flat is to contain 1 table, 4 chairs, 2 beds, and

1 wardrobe.

Let F=

0

B

@

1

4

2

1

1

C

A be the matrix representing the furniture in one flat.

In terms ofF, what is the matrix representing the furniture inallflats? Evaluate this matrix.

4 On weekdays, a video store finds that its average daily hirings are 75 DVD movies, 27 Blu-ray movies,

and 102 games. On weekends, the average daily hirings are 43 Blu-ray movies, 136 DVD movies, and

129 games.

0

@

1

A

DVD movies

Blu-ray movies

games

a Represent the data usingtwocolumn matricesAandB.

b Find 5 A+2B.

c What does the matrix inbrepresent?

5 Isabelle sells clothing made by four different companies which

we will call A, B, C, and D.

Her usual monthly order is:

ABCD

skirt

dress

evening

suit

0

B

@

30 40 40 60

50 40 30 75

40 40 50 50

10 20 20 15

1

C

A

Find her order, to the nearest whole number, if:

a she increases her total order by15%

b she decreases her total order by15%.

ZERO OR NULL MATRIX

Azero matrixis a matrix in which all the elements are zero.

For example, the 2 £ 2 zero matrix is

μ

00

00

¶

, and the 2 £ 3 zero matrix is

μ

000

000

¶

.

IfAis a matrix of any order andOis the correspondingzero matrix, then

A+O=O+A=A.

For example:

μ

23

4 ¡ 1

¶

+

μ

00

00

¶

=

μ

23

4 ¡ 1

¶

and

μ

00

00

¶

+

μ

23

4 ¡ 1

¶

=

μ

23

4 ¡ 1

¶

.

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_12\313CamAdd_12.cdr Tuesday, 7 January 2014 5:56:28 PM BRIAN