If are different numbers and = ! pmatrix x & x^2 & 1+x^3 y & y^2 & 1+y^3 z & z^2 &…

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

x, y, z

are different numbers and

\Delta = \det\!\begin{pmatrix}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{pmatrix} = 0,

then show that

1 + xyz = 0