4.10 SPM Practice (Long Questions)


Question 7:
(a) Find the inverse matrix of (3254).
(b) Ethan and Rahman went to the supermarket to buy cucumbers and carrots. Ethan bought 3 cucumbers and 2 carrots for RM9. Rahman bought 5 cucumbers and 4 carrots for RM16.
By using matrix method, find the price, in RM, of a cucumber and the price of a carrot. 


Solution:
(a)Inverse matrix of (3254)=11210(4253)=12(4253)=(215232)

(b)3x+2y=9.................(1)5x+4y=16...............(2)(3254)(xy)=(916)              (xy)=(215232)(916)              (xy)=((2)(9)+(1)(16)(52)(9)+(32)(16))              (xy)=(1816452+24)              (xy)=(232)x=2,  y=32



Question 8:
The inverse matrix of   ( 4 1 2 5 ) is t( 5 1 2 n ).
(a) Find the value of n and of t.
(b) Write the following simultaneous linear equations as matrix equation:
4xy = 7
2x + 5y = –2
Hence, using matrix method, calculate the value of x and of y.


Solution:
(a) t( 5 1 2 n )= ( 4 1 2 5 ) 1 = 1 ( 4 )( 5 )( 1 )( 2 ) ( 5 1 2 4 ) = 1 22 ( 5 1 2 4 ) t= 1 22 , n=4

(b) ( 4 1 2 5 )( x y )=( 7 2 )   ( x y )= 1 22 ( 5 1 2 4 )( 7 2 )   ( x y )= 1 22 ( ( 5 )( 7 )+1( 2 ) ( 2 )( 7 )+( 4 )( 2 ) )   ( x y )= 1 22 ( 352 148 )   ( x y )= 1 22 (  33 22 )   ( x y )=(   3 2 1 ) x= 3 2 ,  y=1