1. The matrix M is equal to [-4 2; -5 3]. The values of x and y that satisfy the simultaneous equations are x=5 and y=-4. 2. The values of m and p are m=1/2 and p=4. The values of x and y that satisfy the simultaneous equations are x=7 and y=11/2. 3. The values of k and h are k=1/11 and h=5. The values of x and y that satisfy the simultaneous equations are x=-1 and y=3.

1. ppr maths nbk
SPM FORMAT QUESTIONS
PAPER 2
⎛3 − 2⎞ ⎛1 0⎞
1. M is a 2 x 2 matrix where M ⎜
⎜ ⎟ =⎜
⎟ ⎜ ⎟.
⎟
⎝5 − 4⎠ ⎝ 0 1⎠
(a) Find the matrix M
(b) Write the following simultaneous linear equations as matrix equation
3x – 2y = 7
5x – 4y = 9
Hence, calculate the values of x and y using matrices.
⎛3 − 4⎞ ⎛− 6 p⎞
2. (a) The inverse matrix of ⎜
⎜ 5 − 6 ⎟ is m
⎟ ⎜
⎜− 5 ⎟.
⎝ ⎠ ⎝ 3⎟
⎠
Find the value of m and p.
(b) Using matrices, calculate the value of x and of y that satisfy the following
simultaneous linear equations:
3x – 4y = -1
5x – 6y = 2
⎛ 2 − 5⎞ ⎛ 3 h⎞
3. It is given that matrix P = ⎜⎜ 1 3 ⎟ and matrix Q = k ⎜ − 1 2 ⎟ such that
⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
⎛1 0⎞
PQ = ⎜ ⎜0 1⎟ .
⎟
⎝ ⎠
(a) Find the value of k and h.
(b) Using matrices, calculate the value of x and of y that satisfy the following
simultaneous linear equations:
2x – 5y = -17
x + 3y = 8

2. ppr maths nbk
⎛2 1 ⎞ ⎛ − 4 − 1⎞
4. (a) The inverse matrix of ⎜
⎜ 3 − 4 ⎟ is m
⎟ ⎜
⎜ p ⎟.
⎝ ⎠ ⎝ 2⎟⎠
Find the value of m and p.
(b) Using matrices, calculate the value of x and y that satisfy the following
simultaneous linear equations:
2x + y = 4
3x – 4y = 17.
1⎛ 4 1 ⎞ ⎛ − 2 m⎞ ⎛1 0⎞
5. It is given that ⎜
⎜ − 6 − 2⎟ ⎜ 6 4 ⎟ = ⎜0 1⎟ .
⎟⎜ ⎟ ⎜ ⎟
k ⎝ ⎠⎝ ⎠ ⎝ ⎠
(a) Find the value of k.
(b) Find the value of m.
(c) Hence, using matrices, calculate the value of v and w that satisfy the
following matrix equation:
⎛ 4 1 ⎞ ⎛v⎞ ⎛ 8 ⎞
⎜ ⎟⎜ ⎟ = ⎜
⎜ − 6 − 2⎟ ⎜ w⎟ ⎜ − 10 ⎟
⎟
⎝ ⎠⎝ ⎠ ⎝ ⎠
⎛ a 3⎞
6. Given matrix N = ⎜
⎜ 6 9⎟ .
⎟
⎝ ⎠
(a) If the determinant for matrix N is zero, find the value of a.
(b) If a = 1,
(i) find the inverse of matrix N,
(ii) using matrix method, find the values of h and k that satisfy the
following matrix equation :
⎛ 1 3⎞ ⎛ h ⎞ ⎛ − 5⎞
⎜
⎜ 6 9⎟ ⎜ k ⎟ = ⎜ 6 ⎟
⎟ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠ ⎝ ⎠

3. ppr maths nbk
⎛ 6 3⎞ 1 ⎛− 3 3 ⎞
7. If A is the matrix ⎜
⎜ a b ⎟ and the inverse matrix of A is a ⎜ a − 6 ⎟ , find the
⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
values of a and b.
Hence , using matrices, calculate the values of x and y that satisfy the following
simultaneous linear equation:
6x + 3y = 3
Ax + by = 5
⎛5 r ⎞
8. Given matrix G = ⎜ ⎜ 4 − 2⎟ ,
⎟
⎝ ⎠
(a) find the value of r if G does not have an inverse matrix,
(b) find the inverse matrix of G, if r = -2,
(c) calculate by using matrices, the values of v and w that satisfy the following
matrix equation :
⎛ 5 − 2⎞ ⎛ v ⎞ ⎛1⎞
⎜
⎜ 4 − 2⎟ ⎜ w⎟ = ⎜ 2⎟
⎟⎜ ⎟ ⎜ ⎟
⎝ ⎠⎝ ⎠ ⎝ ⎠
⎛ 5 − 3⎞ ⎛ − 2 3⎞
9. (a)Given that the inverse matrix of ⎜
⎜ 4 − 2 ⎟ is m ⎜ p 5 ⎟ , find the values of m
⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
and p.
(b) Using matrices, find the values of x and y that satisfy the following
simultaneous equations.
5x – 3y = 1
4x – 2y = 2
⎛ 4 5⎞ ⎛1 0⎞
10. Given matrix P = ⎜
⎜ 6 8 ⎟ and matrix PQ =
⎟ ⎜
⎜0 1⎟
⎟
⎝ ⎠ ⎝ ⎠
(a) find matrix Q, and
(b) hence, calculate by using matrix method, the values of m and n that
satisfy the following simultaneous linear equations:
4m + 5n = 7
6m + 8n = 1

4. ppr maths nbk
ANSWERS
PAPER 2
1 ⎛ − 4 2⎞
1. (a) M=- ⎜ ⎟
2 ⎜ − 5 3⎟
⎝ ⎠
⎛3 − 2⎞ ⎛ x ⎞ ⎛ 7⎞
(b) ⎜
⎜5 − 4⎟ ⎜ y ⎟ = ⎜ 9⎟
⎟⎜ ⎟ ⎜ ⎟
⎝ ⎠⎝ ⎠ ⎝ ⎠
x=5
y = -4
1
2. (a) m=
2
p=4
(b) x=7
11
y=
2
1
3. (a) k=
11
h=5
(b) x = -1
y=3
1
4. (a) m=-
11
p = -3
(b) x=3
y=-2
5. (a) k = -2
m = -1
(b) v=3
w = -4
6. (a) 2

5. ppr maths nbk
⎛ 1 ⎞
⎜−1 ⎟
(c) (i) ⎜ 3 ⎟
⎜ 2 − 1⎟
⎜ ⎟
⎝3 9⎠
(iii) h = 7, k = -4
2 1
7. a= 9, b = 3, x= ,y= -
3 3
5
8. r=-
2
⎛ 1 − 1⎞
(b) ⎜ 5⎟
⎜2 ⎟
⎝ 2⎠
(c) v =-1, w = − 3
1
9. (a) m = p = -4
2
(b) x = 2, y = 3
⎛ 5⎞
10. (a) ⎜ 4 − ⎟
⎜ 2⎟
⎝ −3 2 ⎠
(b) m = 3, n = -1