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Let |{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)...

Let
`|{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)z^(6)(x^(3)-z^(3)),,x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),,xz^(3)(z^(6)-x^(6)) ,,xy^(2)(x^(6)-y^(6))),(y^(2)^(3)(z^(3)-y^(3)),,xz^(3)(x^(3)-z^(3)),,xy^(2)(y^(3)-x^(3))):}| " and " Delta_(2)= |{:(x,,y^(2),,z^(3)),(x^(4),,y^(5) ,,z^(6)),(x^(7),,y^(8),,z^(9)):}| `.Then `Delta_(1)Delta_(2)` is equal to

A

`Delta_(2)^(6)`

B

`Delta_(2)^(4)`

C

`Delta_(2)^(3)`

D

`Delta_(2)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
the given determinant `Delta_(1)` is obtained by corresponding cofactors or determinant `Delta_(2)` and hence `Delta_(1)= Delta_(2)^(2)`
Now `Delta_(1)Delta_(2) =Delta_(2)^(2) Delta_(2) =Delta_(2)^(2)`
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