Page 18 - Focus SPM KSSM 2021 Tingkatan 5 - Maths DLP

Mathematics Form 5 Chapter 2 Matrices

2. Express each of the following as a single matrix. (c) [7 2] 3 1 –1 4
(a) 3 2 3 4 3 –4 5 4 (d) 3 9 10 3 12
+
1 –9
6 –7
4
43 4
4 –5
1
–
(b) 3 0 3 10 4 3 5 6 1 4 12. Find the product for each of the following.
9
–8 –2
–3 –4 9
3. Given that [–4 9] + T – [5 –2] = [1 –6], find 6 –3 1
matrix T. (a) [3 –4] 3 2 5 –1 4
2
4. Find the values of x and y for each of the following. (b) 3 –7 6 43 4
10
5
–1
8
=
(a) 3 5 2x 4 3 2 5x 4 3 3 9 4 4 2 –3 7 –1 Chapter 2
–
3y 7
8
3

y
1
x
4
(b) 3 3x – 2 4 3 4 3 4 (c) 3 3 4 43 –3 5 4
+
=
7
1 + y
2y
5
Chapter 2
(d) 3 4 [1 3 –4]
5. Express each of the following as a single matrix. –2
1
(a) 3[–5 7] 13. It is given that S = [–4 3], T = 3 4 , U = 3 5 1 4 and
–3 2
–2
3
(b) 1 12 –3 4 V = 3 1 –4 4 . Find
4 8 20 3 6
6. It is given that P = 3 2 6 4 , Q = 3 1 –4 4 and (a) ST
(b) VT
–3 5
8 3
R = 3 –7 9 4 . Find (c) SU
(d) TS
10 –2
2
(a) R + Q (e) U
(b) P + (Q + R) 14. Solve the following equations.
(c) Q – R + P
5
6
=
(a) 3 x –1 43 4 3 4
3 2y
4
–9
–6
4
7. Given that M = 3 4 and N = 3 4 , calculate 3 12 21
2
1
(a) 2(M + N) (b) 3 4 [1 – x 7] = 3 2y –35 4
–5
(b) 0.8(M – N)
15. Write the identity matrices for the following orders.
8. Express each of the following as a single matrix. (a) 2 × 2
(b) 3 × 3
(a) 2 3 2 –1 4 3 4 3 4 16. Determine whether the following matrices are
+
3 12
7 –15
1
(b) [13 4] – 5[3 2] + [12 –8] 4 5
2 identity matrices for 3 3 2 4 .
9. Find matrix U for each of the following. 1 0
1 6 –4 4 (a) 3 0 1 4
(a) 3 4 + 3 3 4 – U = 3 4
3 12 2 1 (b) 3 1 1 4
(b) 2U – 3 10 6 4 = 4 3 4 –2 4 0 0
2
1
9
5
10. Find the values of p and q for each of the following. 17. It is given that M = 3 –1 5 4 , N = 3 3 10 4 and
8
4 –2
6
q
6
3
–
(a) 5 3 4 3 4 3 4 K = 3 5 2 4 . Express each of the following as a
=
–7 1
11
–p
4
=
(b) 3 1 p 4 + 3 3 2 p 4 3 7 –8 4 single matrix.
(a) MI – IN
3
14 11
q – 1
2
5
(b) (K + N)I
11. Determine whether the following pairs of matrices (c) (KI)M
can be multiplied. If yes, state the order of the
product. 18. Determine whether the following matrices are
3
8
1
3 4 inverse matrices of 3 –2 –5 4 .
(a) 9 [2 –1]
8 (a) 3 –5 –8 4
0
(b) [5 –3 4] 3 4 2 3
6
(b) 3 –3 2 4
–8 5
30
02 Focus Math F5_E2021.indd 30 18/02/2021 2:32 PM