UPSC NDA Math Model Paper 2

Given, A=[

x+y	y
2x	x−y

],B=[

2

−1

] and C=[

3

2

]
To find the value of the determinant of matrix A, we need to find x and y first.
Given, AB = C
[

x+y	y
2x	x−y

][

2

−1

] =[

3

2

]
⇒[

2(x+y)−y

4x−x+y

]=[

3

2

]
⇒[

2x+y

3x+y

]=[

3

2

]
The two matrices are equal. Hence, their corresponding elements are also equal.
2x + y = 3....(1)
3x + y = 2....(2)
Solving equation (1) and (2), we get
⇒ x = - 1 and y = 5
Matrix A becomes,A=[

x+y	y
2x	x−y

]=[

4	5
−2	−6

]
Determinant of A becomes, |A|=[

4	5
−2	−6

]=−14