Page 19 - Top Class F5 - Mathematics (Chapter 2)

Mathematics Form 5 Chapter 2 Matrices
23. Find the value of x if T does not have an inverse matrix. PL 4
Cari nilai x jika T tidak mempunyai matriks songsang. If ad – bc = 0, then inverse matrix does not exist.
Jika ad – bc = 0, maka matriks songsang tidak wujud.
Example 6 3 –2 3x x –5
(a) T =   (b) T =   (c) T =  
  2x 2 4 18 –4 2
8 6
T = x 3 6(2) – 3(2x) = 0 (–2)(18) – (3x)(4) = 0 2x – (–5)(–4) = 0
8(3) – 6x = 0 12 – 6x = 0 –36 – 12x = 0 2x – 20 = 0
24 – 6x = 0 6x = 12 12x = –36 2x = 20
6x = 24 x = 2 x = –3 x = 10
x = 4

24. Given that TU = UT = I, find matrix U. PL 4
Diberi TU = UT = I, cari matriks U.

Example 1 0 7 3
(a) T =   (b) T =  –5 –2 
6 8
T =  –10 5 
–4 3
U = T –1 U = T –1

U = T –1 1  8 0  1  –2 –3 

1 3 –5 = =
=   1(8) – 0(6) –6 1 7(–2) – 3(–5) 5 7
(–10)(3) – 5(–4) 4 –10 1 8 0 –2 –3
1 3 –5 =   =  
= –   8 –6 1 5 7
10 4 –10 1 0
 – 10 2  = – 
1
3
3 1
= 2 4 8
–
5 1

25. Find the value of m and of n. PL 4
Cari nilai m dan nilai n.

Example (a) It is given that 1 2 –4  is the inverse matrix of

1 –5 n m –3 n
It is given that   is the inverse matrix of
7 4
m 1 3   .
 –1 –5  . 3 2 1 2 –4 7 4
3 10

1 –5 n 3 10 Diberi m –3 n  ialah matriks songsang bagi   .
3 2
Diberi   ialah matriks songsang bagi   .
m 1 3 –1 –5 7 4
3 10
3 2
Inverse matrix of / Matriks songsang bagi  –1 –5  Inverse matrix of / Matriks songsang bagi  
2 –4
1 –5 –10 = 1  
=   7(2) – 4(3) –3 7
3(–5) – 10(–1) 1 3 1 2 –4
1 –5 –10 =  
= –   2 –3 7
5 1 3
1 2 –4 1 2 –4
1 –5 –10 1 –5 n   =  
–   =   2 –3 7 m –3 n
5 1 3 m 1 3
Hence / Maka, m = –5, n = –10 Hence / Maka, m = 2, n = 7

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