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Q. $\begin{vmatrix}24 & 25 & 26 \\ 25 & 26 & 27 \\ 26 & 27 & 27\end{vmatrix}$ is equal to

EAMCETEAMCET 2011

Solution:

Let $\Delta \begin{vmatrix}24 & 25 & 26 \\ 25 & 26 & 27 \\ 26 & 27 & 27\end{vmatrix}$
Applying $R_{2} \rightarrow R_{2}-R_{1}$
and $R_{3} \rightarrow R_{3}-R_{2}$
$\Delta=\begin{vmatrix}24 & 25 & 26 \\ 1 & 1 & 1 \\ 1 & 1 & 0\end{vmatrix}$
$=1[25-26]-1[24-26]$
$=-1+2=1$