JEE Main 2017 · Mathematics · Matrices and Determinants · medium

The value of the determinant beginvmatrix1&1&1\\1&2&4\\1&3&9endvmatrix is

Single correct option

The value of the determinant

\begin{vmatrix}1&1&1\\1&2&4\\1&3&9\end{vmatrix}

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Answer: (B) $2$

This is a Vandermonde determinant with entries

1,x,x^2

for

x=1,2,3

. Its value is

(2-1)(3-1)(3-2)=1\cdot2\cdot1=2

. Direct expansion:

1(18-12)-1(9-4)+1(3-2)=6-5+1=2

, which agrees. It is non-zero because the three values of

x

are distinct.

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