Question

If Δ = \(\begin{vmatrix} 1 & x& x^2 \\[0.3em] 1 &y & y^2 \\[0.3em] 1 & z &z^2 \end{vmatrix}\) and Δ₁ = \(\begin{vmatrix} 1 & 1 & 1\\[0.3em] yz &zx & xy \\[0.3em]x& y &z\end{vmatrix}\), then prove that Δ + Δ₁ = 0.

Answer 1

Suppose

Any two rows or column of determinant are interchanged, then the sign of determinant also changed.

Hence proved.