NDA 2017 Maths · Mathematics · Determinants · medium

For the determinant Δ=beginvmatrix2&-1&3\\0&4&5\\1&2&-2endvmatrix, the cofactor of the element 3 is

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For the determinant

\Delta=\begin{vmatrix}2&-1&3\\0&4&5\\1&2&-2\end{vmatrix}

, the cofactor of the element 3 is

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Answer: (B) $-4$

The element 3 sits in row 1, column 3, so its sign factor is

(-1)^{1+3}=+1

. Its minor is

\begin{vmatrix}0&4\\1&2\end{vmatrix}=0-4=-4

. So the cofactor is

-4

. Using the wrong sign gives 4.

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