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4.10 SPM Practice (Long Questions)

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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    14    3)(xy)=( 517)            (xy)=11(3)−4(1)(  3    −1−4       1)( 517)            (xy)=−1(3(5)+(−1)(17)−4(5)+(1)(17))            (xy)=−1(15−17−20+17)            (xy)=−1(−2−3)            (xy)=(23)x=2 and y=3



Question 12 (6 marks):
Given A=(4    −23    −1), B=m(−1    n−3    4)and I=(1    00    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
3x – y = 2
Hence, by using matrix method, calculate the value of x and of y.

Solution:
(a)
If AB=I, then B=A−1A−1=14(−1)−(−2)(3)(−1    2−3    4)A−1=12(−1    2−3    4)By comparison:B=A−1m(−1    n−3    4)=12(−1    2−3    4)m=12 ; n=2


(b)
4x−2y=33x−y=2(4    −23    −1)(xy)=(32)               (xy)=12(−1    2−3    4)(32)               (xy)=12((−1)(3)+(2)(2)(−3)(3)+(4)(2))               (xy)=12(  1−1)               (xy)=(  12−12)x=12 and y=−12