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3 and 4 .Determinants and Matrices
easy
The value of the determinant $\left| {\,\begin{array}{*{20}{c}}4&{ - 6}&1\\{ - 1}&{ - 1}&1\\{ - 4}&{11}&{ - 1\,}\end{array}} \right|$is
A
$-75$
B
$25$
C
$0$
D
$-25$
Solution
(d) $\left| {\,\begin{array}{*{20}{c}}4&{ – 6}&1\\{ – 1}&{ – 1}&1\\{ – 4}&{11}&{ – 1}\end{array}\,} \right| = \left| {\,\begin{array}{*{20}{c}}0&5&0\\{ – 1}&{ – 1}&1\\{ – 4}&{11}&{ – 1}\end{array}\,} \right|$ $\{ {\rm{Apply }}\,{R_{\rm{1}}} \to {R_1} + {R_3}\} $
= $ – 5\,(1 + 4) = – 25$.
Standard 12
Mathematics