Question 12:
(a) It is given that matrix H=(261k).
Solution:
(a)
Given that matrix H does not have inverse matrix, ad−bc=02(k)−6(1)=02k−6=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+9−3x−3y=6…(2)[111−3][xy]=[346][xy]=11(−3)−1(1)[−3−1−11][346]=−14[−3(34)−1(6)−1(34)+1(6)]=−14[−108−28]=[277]
(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).
(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, ad−bc=02(k)−6(1)=02k−6=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+9−3x−3y=6…(2)[111−3][xy]=[346][xy]=11(−3)−1(1)[−3−1−11][346]=−14[−3(34)−1(6)−1(34)+1(6)]=−14[−108−28]=[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).