Mathematics 9 (Complete Solutions)

Q2
Find the determinant of the following matrices.

(i) A =
 
3 6
2 4
 
(ii) B =
 
4 1
3 2
 
(iii) C =
 
7 -9
3 5
 
(iv) D =
 
5 -10
-2 4
 
Solution:


(i) A =
 
3 6
2 4
 
∣ A ∣ =
3 6
2 4
∣ A ∣ = (3)(4) - (6)(2)
∣ A ∣ = 12 - 12
∣ A ∣ = 0

A is singular matrix


(ii) B =
 
4 1
3 2
 
∣ B ∣ =
4 1
3 2
∣ B ∣ = (4)(2) - (1)(3)
∣ B ∣ = 8 - 3
∣ B ∣ = 5

B is non-singular matrix


(iii) C =
 
7 -9
3 5
 
∣ C ∣ =
7 -9
3 5
∣ C ∣ = (7)(5) - (-9)(3)
∣ C ∣ = 35 + 27
∣ C ∣ = 62

C is non-singular matrix


(iv) D =
 
5 -10
-2 4
 
∣ D ∣ =
5 -10
-2 4
∣ D ∣ = (5)(4) - (-10)(-2)
∣ D ∣ = 20 - 20
∣ D ∣ = 0

D is singular matrix

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