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  4. The value of the determinant |265&240&219 240&225&198 219&198&181| is

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Q. The value of the determinant $\begin{vmatrix}265&240&219\\ 240&225&198\\ 219&198&181\end{vmatrix}$ is

BITSATBITSAT 2012

Solution:

Applying $C_{1} -C_{2}$ and $ C_{2} -C_{3},$ we get
Det.$ = \begin{vmatrix}25&21&219\\ 15&27&198\\ 21&17&181\end{vmatrix} = \begin{vmatrix}4&21&9\\ -12&27&-72\\ 4&17&11\end{vmatrix}$
$ \left[\text{by} C_{1} -C_{2} , C_{3} - 10 C_{2}\right] $
$ = \begin{vmatrix}4&21&9\\ 0&90&-45\\ 0&-4&2\end{vmatrix} \left[\text{By} R_{2} + 3R_{1} , R_{3} - R_{1}\right] $
$= 4 (180 - 180) = 0$