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