Question

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

• A. 1000
• B. 779
• C. 679
• D. 0

Answer 1

Answer: (D)

0

Answer 2

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