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