Cambridge Additional Mathematics

332 Matrices (Chapter 12)

8 For A=

μ

32

¡ 11

¶

, find:

a detA b det (¡ 2 A) c det (A^2 )

9 Solve using an inverse matrix:

a

½

x+y=5

x¡ 2 y=4

b

½

3 x+2y=3

5 x+3y=4

10 If M=

μ

k 2

2 k

¶μ

k¡ 1 ¡ 2

¡ 3 k

¶

has an inverseM¡^1 , what values cankhave?

11 For what values ofkdoes the system

½

kx+3y=¡ 6

x+(k+2)y=2

have a unique solution?

State the solution in this case.

12 Write 5 A^2 ¡ 6 A=3I in the form AB=I. Hence writeA¡^1 in terms ofAandI.

13 Prove that for any 2 £ 2 matrixA, A^2 can be written in the linear form aA+bI.

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100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_12\332CamAdd_12.cdr Wednesday, 8 January 2014 9:45:39 AM BRIAN