Question

Evaluate: `|(0, xy^2, xz^2),(x^2y, 0, yz^2),(x^2z, zy^2, 0)|`

Answer 1

We have, `|(0, xy^2, xz^2),(x^2y, 0, yz^2),(x^2z, zy^2, 0)|`

[Taking x², y² and z² common from C₁, C₂ and C₃, respectively]

= `x^2y^2z^2|(0, x, x),(y, 0, y),(z, z, 0)|`

[Applying C₁ → C₂ – C₃]

 = `x^2y^2z^2|(0, 0, x),(y, -y, y),(z, z, 0)|`

= `x^2y^2z^2 (x(yz + yz))`

= `x^2y^2z^2 * (2xyz)`

= 2x³y³z³