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  4. |101&103&105 104&105&106 107&108&109| =

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Q. $\begin{vmatrix}101&103&105\\ 104&105&106\\ 107&108&109\end{vmatrix} = $

COMEDKCOMEDK 2008Determinants

Solution:

$\begin{vmatrix}101&103&105\\ 104&105&106\\ 107&108&109\end{vmatrix} $
$= \begin{vmatrix}100+1&100+3&100+5\\ 100+4&100+5&100+6\\ 100+7&100+8&100+9\end{vmatrix}$
$= \begin{vmatrix}100&100&100\\ 100&100&100\\ 100&100&100\end{vmatrix}+\begin{vmatrix}1&3&5\\ 4&5&6\\ 7&8&9\end{vmatrix}$
$( \because$ All rows are identical $)$
$ = 0 + [ -3+ 18 - 15 ] = 0 $