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3 and 4 .Determinants and Matrices
easy
If ${\Delta _1} = \left| {\,\begin{array}{*{20}{c}}1&0\\a&b\end{array}\,} \right|$ and ${\Delta _2} = \left| {\begin{array}{*{20}{c}}1&0\\c&d\end{array}} \right|$, then ${\Delta _2}{\Delta _1}$is equal to
A
$ac$
B
$bd$
C
$(b - a)(d - c)$
D
None of these
Solution
(b) ${\Delta _2}{\Delta _1} = \left| {\begin{array}{*{20}{c}}1&0\\c&d\end{array}} \right|\,\,\left| {\,\begin{array}{*{20}{c}}1&0\\a&b\end{array}\,} \right| = \left| {\,\begin{array}{*{20}{c}}1&0\\{c + ad}&{bd}\end{array}\,} \right| = bd$.
Standard 12
Mathematics