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