Q13 of 45 Page 1

Using properties of determinants, prove the following:

Let,


Δ =


To prove: Δ = 9y2(x + y)


Applying C1 → C1 + C2 + C3, we get-


Δ =


Taking (3x +3y) common from first column, we get


Δ =


Applying R1 → R1 – R2, we get-


Δ =


Applying R2 → R2 – R3, we get-


Δ =


Expanding about 3rd row –


Δ = 3(x + y)


⇒ Δ = 3(x + y)(y2 + 2y2)


⇒ Δ = 9y2(x + y)


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