4.10 SPM Practice (Long Questions)


Question 9:
(a) Given 1s(4253)(t254)=(1001), find the value of s and of t.

(b) Using matrices, calculate the value of x and of y that satisfy the following matrix equation:
(4253)(xy)=(12)


Solution:
(a)1s(t254)=(4253)1=1(4)(3)(2)(5)(3254)=12(3254)s=2, t=3

(b)(4253)(xy)=(12)  (xy)=12(3254)(12)  (xy)=12((3)(1)+(2)(2)(5)(1)+(4)(2))  (xy)=12(13)  (xy)=(1232)x=12,  y=32



Question 10 (5 marks):
During the sport day, students used coupons to buy food and drink. Ali and Larry spent RM31 and RM27 respectively. Ali bought 2 food coupons and 5 drinks coupons while Larry bought 3 coupons and 1 drinks coupon.
Using the matrix method, calculate the price, in RM, of a food coupon and of a drinks coupon.

Solution:
Ali spent RM31. He bought 2 food coupons and 5 drinks coupons.
Larry spent RM27. He bought 3 food coupons and 1 drinks coupons.
x = price of one food coupon
y = price of one drinks coupon

(2    53    1)(xy)=(3127)            (xy)=12(1)5(3)(1    53     2)(3127)            (xy)=1215(1(31)+(5)(27)3(31)+2(27))            (xy)=113(10439)            (xy)=(83)x=8 and y=3Thus, the price for a food coupon is RM8and the price for drink coupon is RM3.