Page 30 - Past Year

28 | P a g e

 1 2   0  2 4

(b) Given P    5 4 and Q    , determine matrix R such that

 3  2    1 3 2 
 

 2  2 5


T
PQ   R   1 4 1 .


 
 0 3 4 

31. Table below shows the floor area of the rooms in Amir’s house.
Room Floor Area (square metre)

Living room 25

Bedroom 1 15
Bedroom 2 10

Bedroom 3 10
Kitchen 10

Amir intends to replace his home floor to ceramic tiles, parquet or mosaic. If he uses

ceramic tiles for the living room, parquet for all the bedrooms and mosaic for the kitchen,

the total cost is RM 2625. If he uses ceramic tiles for the living room and bedroom 1, and
mosaic for the other bedrooms and kitchen, the total cost is RM 2450. However, if

bedrooms 2 and 3 use parquet, and other rooms and kitchen use ceramic tiles, the total cost
is RM 3200.

Let the prices per square metre of ceramic tiles, parquet and mosaic be x, y and z
respectively.

(a) Obtain a system of linear equations to represent the given information. Hence, state
B
the equations in the form of AX  .
(b) Based on (a), find the inverse of matrix A. Hence, determine the price (RM) per

square meter for each ceramic tiles, parquet and mosaic.