Q13 of 45 Page 1

Using properties of determinants, prove that

Let


R3→ (-1)R3



R2→ 2R2



R3→ R3 + R2



Expand determinant along 3rd row


⇒ Δ = -1/2[x(8x(x + y) – x(10x + 8y))]


⇒ Δ = -1/2x[8x2 + 8xy – 10x2 – 8xy]


⇒ Δ = -1/2x[8x2 – 10x2]


⇒ Δ = -1/2x[–2x2]


⇒ Δ = x3


Hence proved.


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