Page 11 - Top Class F5 - Mathematics (Chapter 2)

Mathematics Form 5 Chapter 2 Matrices

–5
(c) [4 1 –8] + [3 –4 5] (d)       (e) [2p 3q] + [4p 1]
3
6
+
= [4 + 3 1 + (–4) –8 + 5] –1 2 – 18 = [ 2p + 4p 3q + 1]
= [7 –3 –3] 6 + 3 – (–5) = [6p 3q + 1]
=  –1 + 2 – 18 
 
14
= –17
 2 10   6 –1   –5 –8  5x 3x –2x
(f) –3 7 – 4 9 + 2 3 (g)      
–
–
8y
y + 1
5
 2 – 6 + (–5) 10 – (–1) + (–8)  4z –2 3
= –3 – 4 + 2 7 – 9 + 3 5x – 3x – (–2x)
=  –9 3  =  y + 1 – 5 – 8y 
–5 1
4z – (–2) – 3
 4x 
= –4 – 7y
4z – 1

 9 11   –6 3   14 2 
7. Given that P = 2 –4 , Q = 5 8 and R = –7 –1 , solve each of the following. PL 3
 9 11   –6 3   14 2 
Diberi P = 2 –4 , Q = 5 8 dan R = –7 –1 , selesaikan setiap yang berikut.

Example (a) Q + P (b) P – Q
P + Q  –6 3   9 11   9 11   –6 3 
+
–
 9 11   –6 3  5 8 2 –4 2 –4 8 5 8
+
2 –4
5 8
3 14
15
 3 14  =  7 4  =  –3 –12 
= 7 4
(c) Q – P (d) (P + Q) + R (e) P + (Q + R)
 –6 3   9 11  9 11 –6 3 14 2 9 11 –6 3 14 2
5 8 – 2 –4  2 –4   5 8   –7 –1   2 –4   5 8   –7 –1 
+
+
+
+
 –15 –8  3 14 14 2 =  9 11   8 5 
+
= 3 12 =  7 4   –7 –1  2 –4 –2 7
+
=  17 16  =  17 16 
0
3
3
0
Conclusion / Kesimpulan:
P + Q = Q + P P – Q  Q – P (P + Q) + R = P + (Q + R)

8. Calculate the value of x and of y for each of the following. PL 3
Hitung nilai x dan nilai y bagi setiap yang berikut.

Example 5 3x – 2 1 4 6 x
=
(a)      
+
x
10 11
7
 4y + 1 6   3 2x   4 –1  –3 4 – 2y 3x – 2 + 4 7 3y
–
=
8
y
7 –2
6 x
5 + 1
=
7 – 3
 4y + 1 – y 6 – 8   4 –1   –3 + 10 4 – 2y + 11   7 3y 
x – 2x
=
7 –2
x – 2x = –1 , 4y + 1 – y = 7 3x – 2 + 4 = x , 4 – 2y + 11 = 3y
5y = 15

2x = –2
–x = –1 3y = 6 x = –1 y = 3
x = 1 y = 2
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