Cambridge Additional Mathematics

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