Cambridge Additional Mathematics

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330 Matrices (Chapter 12)

Review set 12A


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1 If A=

μ
32
0 ¡ 1


and B=

μ
10
¡ 24


, find:

a A+B b 3 A c ¡ 2 B d A¡B
e B¡ 2 A f 3 A¡ 2 B g AB h BA
i A¡^1 j A^2 k ABA l (AB)¡^1

2 Finda,b,c, anddif:

a

μ
ab¡ 2
cd


=

μ
¡a 3
2 ¡c ¡ 4


b

μ
32 a
b ¡ 2


+

μ
b ¡a
cd


=

μ
a 2
26


3 WriteYin terms ofA,B, andC:
a B¡Y=A b 2 Y+C=A c AY=B
d YB=C e C¡AY=B f AY¡^1 =B

4 Susan keeps 3 hens in a pen. She calls them Anya, Betsy,
and Charise. Each week the hens lay eggs according to
the matrix

L=

0

@

a
b
c

1

A.

Write, in terms ofL, a matrix to describe:
a the eggs laid by the hens over a 4 week period
b the eggs each hen loses each fortnight when Susan
collects the eggs.

5 Suppose A=

μ
¡ 23
4 ¡ 1


, B=

μ
¡ 79
9 ¡ 3


, and C=

μ
¡ 103
021


.

Evaluate, if possible:
a 2 A¡ 2 B b AC c CB

6 Given that all matrices are 2 £ 2 andIis the identity matrix, expand and simplify:
a A(I¡A) b (A¡B)(B+A) c (2A¡I)^2

7 If A^2 =5A+2I, writeA^3 andA^4 in the form rA+sI.

8 If A=

μ
2 ¡ 1
32


, find constantsaandbsuch that A^2 =aA+bI.

9 Find, if possible, the inverse matrix of:

a

μ
68
57


b

μ
4 ¡ 3
8 ¡ 6


c

μ
11 5
¡ 6 ¡ 3


10 For what values ofkdoes

½
x+4y=2
kx+3y=¡ 6

have a unique solution?

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_12\330CamAdd_12.cdr Wednesday, 8 January 2014 9:40:53 AM BRIAN

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