Page 23 - Past Year

21 | P a g e

 1 2 1  2 2  3


12. (a) Given the matrices P    2 1 2 and Q    2  1 0 . Find PQ and


  1 2 2    3 0 3  

hence, determine P .
1

(b) The following table shows the quantities (kg) and the amount paid (RM) for the

three types of items bought by three housewives in a supermarket.

Housewives Sugar (kg) Flour (kg) Rice (kg) Amount Paid (RM)
Aminah 3 6 3 16.50
Malini 6 3 6 21.30
SweeLan 3 6 6 21.00
The prices in RM per kilogram (kg) of sugar, flour and rice are x, y and z
respectively.

(i) Form a system of linear equations from the above information and write the
system of linear equations in the form of matrix equation AX  B

(ii) Rewrite AX  B above in the form kPX  , where A  kP( P is the
B
matrix in (a) and k is a constant. Determine the value of k and hence

find the values of x, y and z.

0  1 1 

13. Matrix A is given by A    5 1  1 .

 2   3  3 

(a) Find

(i) the determinant of A,
(ii) the minor of A and

(iii) the adjoint of A.

1
(b) Based on part (a) above, find A . Hence, solve the simultaneous equations
3
y  z 
2
z
y
5x    9
3
2x  3y  3z 
2