Page 22 - Past Year

20 | P a g e

8. (a) Matrices A and B are given as

 1 2  3  4 1   4

A   1 0 4 , B   1 1 5 . 3 
   
 0 2  2   1 1 1  


-1
Find AB and hence find A .

(b) A company produces three grades of mangoes: X, Y, and Z. The total profit from
1 kg of grade X, 2 kg of grade Y and 3 kg of grade Z mangoes is RM20. The profit

from 4 kg of grade Z mangoes is equal to the profit from 1 kg of grade X mangoes.

The total profit from 2 kg of grade Y and 2 kg of grade Z mangoes is RM10.
(i) Obtain a system of linear equations to represent the given information

(ii) Write down the system in (i) as a matrix equation.
(iii) By using the result from part (a), solve the system of linear equation. Hence,

state the profit per kg for each grade.

  1 0  2  1  1 2 



9. Given A   2 1 0 , B   1 0 and C    1  0   .




  1 1 0   2  1  3 0 1 



T
(a) Find matrix D = A – (BC) .
(b) Show that AD  DA

 1  2 1  0  1  0 2 2




10. If P = 1 1 and Q=   , find matrix R such that R  2PQ   2 4 3 .
   0  1 0   
 0   1    4 5 3 
 
 1 0 0 
  2 0 0   

11. Given A =    4 6  2 and B =    1 1  1  . Show that AB = kI. Where k is a

5
  6  4  2   5 
 1  2  3 
 5 5

1
constant and I is an identity matrix. Find the value of k and hence obtain A