NDA 2020 Maths · Mathematics · Matrices · hard

The value of beginvmatrix1&1&1\a&b&c\a^2&b^2&c^2endvmatrix for a=1, b=3, c=6 is

Single correct option

The value of

\begin{vmatrix}1&1&1\\a&b&c\\a^2&b^2&c^2\end{vmatrix}

for

a=1,\,b=3,\,c=6

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Answer: (C) 30

This is a Vandermonde determinant equal to

(b-a)(c-a)(c-b)=2\cdot5\cdot3=30

. Reversing the order of the factors changes the sign, so

-30

is the trap. Direct expansion confirms it.

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