Question
Using cofactors of elements of third column, evaluate $\Delta=\left|\begin{array}{ccc}1 & x & y z \\ 1 & y & z x \\ 1 & z & x y\end{array}\right|$
= yz( z - y) + zx( x - z) + xy( y - x)
= yz2 - y2z + zx2 - z2x + xy2 - x2y
= zx2 - x2y + xy2 - z2x + yz2 - y2z
= x2 ( z- y) + x(y2 - z2) + yz(z - y)
= (z - y)[ x2 - x( z + y) + yz]
= (z - y)[x2 - xz - xy +yz]
= (z - y) [ x(x - y) - z(x - y)]
= (z - y)[ ( x - y)(x - z)]
= (z - y)( x - y) (x - z)
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.