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UPSC NDA Math Model Paper 8

Question : 79 of 120

Marks: +1, -0

\begin{vmatrix} 2 & 7 & 37 \\ 3 & 6 & 33 \\ 4 & 5 & 29 \end{vmatrix}

Solution:

\begin{vmatrix} 2 & 7 & 37 \\ 3 & 6 & 33 \\ 4 & 5 & 29 \end{vmatrix}

Apply

\mathrm{C}_2 \rightarrow 5\mathrm{C}_2+\mathrm{C}_1

, we get

\begin{vmatrix} 2 & 37 & 37 \\ 3 & 33 & 33 \\ 4 & 29 & 29 \end{vmatrix}

As we can see that the second and the third column of the given matrix are equal.

We know that, if any two rows (columns) of a matrix are same then the value of the determinant is zero.

\therefore \begin{vmatrix} 2 & 7 & 37 \\ 3 & 6 & 33 \\ 4 & 5 & 29 \end{vmatrix} = 0

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