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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(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_12\332CamAdd_12.cdr Wednesday, 8 January 2014 9:45:39 AM BRIAN