Cambridge Additional Mathematics

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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


.

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