4.10 SPM Practice (Long Questions)


Question 11 (5 marks):
Table 8 shows the information of books purchased by Maslinda.
 
Table 8

Maslinda purchased x history books and y Science books. The total number of books purchased is 5. The total price of the books purchased is RM17.

(a)
 Write two linear equations in terms of x and y to represent the above information.

(b)
 Hence, by using matrix method, calculate the value of x and of y.


Solution:
(a)
x + y = 5
4x + 3y = 17

(b)
( 1    1 4    3 )( x y )=(  5 17 )             ( x y )= 1 1( 3 )4( 1 ) (   3    1 4       1 )(  5 17 )             ( x y )=1( 3( 5 )+( 1 )( 17 ) 4( 5 )+( 1 )( 17 ) )             ( x y )=1( 1517 20+17 )             ( x y )=1( 2 3 )             ( x y )=( 2 3 ) x=2 and y=3



Question 12 (6 marks):
Given A=( 4    2 3    1 ), B=m( 1    n 3    4 ) and I=( 1    0 0    1 ).
(a) Find the value of m and of n if AB = I.
(b) Write the following simultaneous linear equation as matrix equation:
4x – 2y = 3
3xy = 2
Hence, by using matrix method, calculate the value of x and of y.

Solution:
(a)
If AB=I, then B= A 1 A 1 = 1 4( 1 )( 2 )( 3 ) ( 1    2 3    4 ) A 1 = 1 2 ( 1    2 3    4 ) By comparison: B= A 1 m( 1    n 3    4 )= 1 2 ( 1    2 3    4 ) m= 1 2  ; n=2


(b)

4x2y=3 3xy=2 ( 4    2 3    1 )( x y )=( 3 2 )                ( x y )= 1 2 ( 1    2 3    4 )( 3 2 )                ( x y )= 1 2 ( ( 1 )( 3 )+( 2 )( 2 ) ( 3 )( 3 )+( 4 )( 2 ) )                ( x y )= 1 2 (   1 1 )                ( x y )=(    1 2 1 2 ) x= 1 2  and y= 1 2