Matrices (Chapter 12) 319
7 At a fair, tickets for the Ferris wheel are $ 12 : 50 per adult and
$ 9 : 50 per child. On the first day of the fair, 2375 adults and
5156 children ride this wheel. On the second day, 2502 adults
and 3612 children ride the wheel.
a Write the costs as a 2 £ 1 matrixC, and the numbers as a
2 £ 2 matrixN.
b FindNCand interpret the resulting matrix.
c Find the total income for the two days.
8 You and your friend each go to your local hardware stores A and B to price items you wish to purchase.
You want to buy 1 hammer, 1 screwdriver, and 2 cans of white paint. Your friend wants 1 hammer,
2 screwdrivers, and 3 cans of white paint. The prices of these goods are:
Hammer Screwdriver Can of paint
Store A $ 7 $ 3 $ 19
Store B $ 6 $ 2 $ 22
a Write the requirements matrixRas a 3 £ 2 matrix.
b Write the prices matrixPas a 2 £ 3 matrix.
c FindPR.
d Find:
i your costs at store A ii your friend’s costs at store B.
e Do any of the elements ofPRtell you and your friend the cheapest way to buy all your items?
Explain your answer.
PROPERTIES OF MATRIX MULTIPLICATION
Discovery 1 Matrix multiplication
#endboxedheading
In this Discovery we find the properties of 2 £ 2 matrix multiplication which are like those of ordinary
number multiplication, and those which are not.
What to do:
1 For ordinary arithmetic 2 £3=3£ 2 , and in algebra ab=ba.
For matrices, doesABalways equalBA?
Hint: Try A=
μ
10
12
¶
and B=
μ
¡ 11
03
¶
.
2 If A=
μ
ab
cd
¶
and O=
μ
00
00
¶
, find AO and OA.
3 FindABfor:
a A=
μ
10
00
¶
and B=
μ
00
01
¶
b A=
μ
4 ¡ 2
¡ 21
¶
and B=
μ
1 ¡ 3
2 ¡ 6
¶
4 For all real numbersa,b, andc, we have thedistributive law a(b+c)=ab+ac.
a Use any three 2 £ 2 matricesABandCto verify that A(B+C)=AB+AC
4037 Cambridge
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Y:\HAESE\CAM4037\CamAdd_12\319CamAdd_12.cdr Tuesday, 7 January 2014 5:57:13 PM BRIAN