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NDA 2016 Maths · Mathematics · Determinants · easy

The cofactor of the element 5 in the matrix beginpmatrix1&2&3\\4&5&6\\7&8&10endpmatrix is

Single correct option

The cofactor of the element 55 in the matrix (1234567810)\begin{pmatrix}1&2&3\\4&5&6\\7&8&10\end{pmatrix} is
  1. A. 1111
  2. B. −2-2
  3. C. 55
  4. D. −11-11
Show answer and solution

Answer: (D) −11-11

The element 5 is in position (2,2)(2,2), so the sign factor is (−1)2+2=+1(-1)^{2+2}=+1. The minor is ∣13710∣=10−21=−11\begin{vmatrix}1&3\\7&10\end{vmatrix}=10-21=-11. Hence the cofactor is −11-11. Taking 1111 results from taking the absolute value of the minor.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake