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SPM Mathematics Trial 2024 (Selangor Set 2), Paper 2 (Question 12)


Question 12:
(a)  It is given that matrix H=(261k)

(a) Find the value of k, if the inverse matrix of H does not exist. [2 marks]

(b)(i) In this year, sum of Puan Mariam’s age and her son’s age is 34 . Three years later, Puan Mariam’s age will be triple her son’s age.
By using matrix method, calculate the age of Puan Mariam and her son this year. [5 marks]

(b)(ii) Puan Mariam plans to retire at the age of 55 and she expects that her son will finish his education at the age of 25 . Based on your answer in 12(b)(i), will her son be able to finish his studies before she retires? Justify your answer. [2 marks]


Solution:
(a)

 Given that matrix H does not have inverse matrix, adbc=02(k)6(1)=02k6=02k=6k=3


(b)(i)
Let, x = age of Puan Mariam
y = age of her son

Given that the sum of Puan Mariam’s age and her son’s age is 34.
x + y = 34 ….. (1)

3 years later, Puan Mariam’s age will be 3 times her son’s age.
x+3=3(y+3)x=3y+93x3y=6(2)[1113][xy]=[346][xy]=11(3)1(1)[3111][346]=14[3(34)1(6)1(34)+1(6)]=14[10828]=[277]

Age of Puan Mariam is 27 and her son is 7 this year.


(b)(ii)
Age of Puan Mariam when her son finishes her study
= 27 + (25 – 7)
= 45 years old

Yes, Puan Mariam’s age when her son finishes his studies is 45 years old (before her retirement).

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