1. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
109
Q10 MATRICES
1 (a) Cari nilai k, jika 





62
1 k
tidak mempunyai songsangan.
(b) (i) Find the inverse matrix of 





62
21
.
(ii) Hence, using matrices, find the value of x and of y that satisfy the following matrix equation :






62
21






y
x
= 





4
1
. (Ans : x = 1, y = 1)
[6 marks]
Answer :
(a)
(b) (i)
(ii)

2. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
110
2 Given that matrix P = 




 
31
4k
and matrix Q = 







11
53
.
(a) Find the value of k, if P does not have an inverse. (Ans : 3
4 )
(b) Find the inverse matrix of Q. (Ans :










2
3
2
1
2
5
2
1
)
(c) If Q 





y
x
= 





2
14
, find the values of x and y using matrices. (Ans : x = 2, y = 4)
[6 marks]
Answer :
(a)
(b)
(c)

3. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
111
3 (a) It is given that 





 m3
25
is the inverse matrix of 




 
n3
21
.
Find the value of m and of n. (Ans : m = 1, n = 5)
(b) Write the following simultaneous linear equations as matrix equation :
5x + 2y = 4
3x  y = 3
Hence, calculate the value of x and of y. (Ans : x = 2, y = 3)
[6 marks]
Answer :
(a)
(b)

4. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
112
4 (a) The inverse matrix of









nm
1
2
1
is 







13
24
.
Find the values of m and n. (Ans : m =  2
3
, n = 2)
(b) Using matrices, calculate the value of x and of y that satisfy the following simultaneous linear
equations :
4x  2y = 10
3x  y = 6 (Ans : x = 1, y = 3)
[6 marks]
Answer :
(a)
(b)

5. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
113
5 (a) The inverse matrix of 







65
43
is m 







35
6 p
.
Find the value of m and of p. (Ans : m = 2
1
, p = 4)
(b) Using matrices, calculate the value of x and of y that satisfy the following simultaneous linear
equations :
3x  4y = 1
5x  6y = 2 (Ans : x = 7, y = 5.5)
[6 marks]
Answer : [2004, No.8]
(a)
(b)

6. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
114
6 Given that matrix 






1
2
n
m
M .
(a) If M1 = 







2
31
8
1
n
, find the values of m and n. (Ans : m = 3, n = 2)
(b) Hence, find the value of h and of k that satisfy the matrix equation 












8
16
k
h
M using matrices.
(Ans : h = 5, k = 2)
[6 marks]
Answer :
(a)
(b)

7. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
115
7 Given that matrix M = 







25
36
, and the inverse matrix of M is 





 65
3
15
1 a
ab
.
(a) Find the value of a and of b. (Ans : a = 2, b = 6)
(b) Hence, using matrices, find the value of e and of f that satisfy the matrix equation 











2
0
f
e
M .
(Ans : e = 2, f = 4)
[6 marks]
Answer :
(a)
(b)

8. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
116
8 Given that the simultaneous linear equations, 2p + 7q = 2 dan 3p + 8q = 3 is write as F 











3
2
q
p
, where
F is a matrix.
(a) Find matrix F. (Ans : 





83
72
)
(b) Given that 




















3
2
3
7
5
1
n
m
q
p
.
(i) Find the value of m and of n. (Ans : m = 8, n = 2)
(ii) Hence, using matrices, find the values of p and q. (Ans : p = 5
37
, q = 5
12 )
[6 marks]
Answer :
(a)
(b) (i)
(ii)

9. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
117
9 (a) Given that matrix R is 







23
47
.
Find matrix Q such that RQ = 





10
01
. (Ans :










2
7
2
3
21
)
(b) Using matrices, find the value of p and of q that satisfy the following simultaneous linear equations :
7p + 4q = 13
3p + 2q = 7 (Ans : ; p = 1, q = 5)
[6 marks]
Answer :
(a)
(b)

10. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
118
10 Given that matrix P = 





32
53
.
(a) If PQ = QP = I, find matrix Q. (Ans : 







32
53
(b) Hence, using matrices, find the value of x and of y that satisfy the following simultaneous linear
equations :
3s + 5t = 8
2s + 3t = 6 (Ans : s = 6, t = 2)
[6 marks]
Answer :
(a)
(b)

11. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
119
11 Given that matrix P = 





 12
31
, matrix R = 




 
1
311
km
, and matrix PR = 





10
01
.
(a) Find the value of k and of m. (Ans : m = 5, k = 2)
(b) Hence, find the value of x and of y that satisfy the following matrix equation :



















 5
5
12
31
y
x
(Ans : x = 2, y = 1)
[6 marks]
Answer :
(a)
(b)

12. [ SM. ST. PETER TELIPOK ] [ LEE CHIONG TEE ] [ MATHEMATICS 1449 / 2 ]
120
12 (a) Given that 





















10
01
62
7
42
761 s
r
.
Find the value of r and of s. (Ans : r = 10, s = 4)
(b) Hence, using matrices, find the value of x and of y that satisfy the following matrix equation :




















6
3
42
76
y
x
(Ans : x = 3, y = 3)
[6 marks]
Answer :
(a)
(b)