Using the properties of determinants in evaluate:

Let

Expanding |A| along C1, we get




= 0 – xy2 [(x2y)(0) – (x2z)(yz2)] + xz2 [(x2y)(zy2) – 0]


= – xy2 [– (x2yz3)] + xz2 [(x2zy3)]


= x3y3z3 + x3z3y3


= 2x3y3z3


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