NDA 2016 Maths · Mathematics · Determinants · medium

The value of the determinant beginvmatrix1&1&1\\1&2&4\\1&4&16endvmatrix is

Single correct option

The value of the determinant

\begin{vmatrix}1&1&1\\1&2&4\\1&4&16\end{vmatrix}

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Answer: (B) $6$

The rows are

(1,a,a^2)

for

a=1,2,4

, a Vandermonde determinant equal to

(2-1)(4-1)(4-2)=1\cdot3\cdot2=6

. The order of subtraction matters: reversing it gives

-6

. Direct expansion along the first row gives

(32-16)-(16-4)+(4-2)\cdot

with the same total.

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