Page 31 - Past Year

29 | P a g e

 1 3  2

32. Given P    2 0 m . Find m if P   1.

  1  2 1  

 1 0   1  1

T
1
33. Given A    and B    .
 2 1   4 2 

T
Find (i)  AB ,
  3 8
(ii) matrix C such that CAB   
 1 2 

3   2 5   3

34. Given 2P Q    2 1   and 3P Q   4 2   . Find matrices P and Q.

  4 5     5 6  

35. The table shows the weight (in kilograms) of three types of fruits namely mango, pineapple
and watermelon which were supplied by a supplier to three restaurants K, L and M on a
daily basis.

Fruits (kg)
Restaurants
Mango Pineapple Watermelon

K 5 5 5

L 10 15 10

M 10 15 15

The payment received by the supplier from the K, L and M restaurants are RM66, RM147
and RM143 respectively. If x, y and z are the prices for each kilograms of the fruits,

(a) state a system of linear equations for the above information given above. Hence,
write in the form of matrix equation, AX = B.

(b) Based on (a), find the inverse matrix of A. Hence, find the price per kilograms for
each of the fruits.

 2 3  2  1  1 1


T
1
1
36. (a) Given A    and C    where A B C    . Find .
 2 4   1 1   0 3 