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3 and 4 .Determinants and Matrices
easy
Find values of ${x},$ if $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{ll}x & 3 \\ 2 x & 5\end{array}\right|$
A
$x=2$
B
$x=3$
C
$x=4$
D
$x=5$
Solution
$\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{ll}x & 3 \\ 2 x & 5\end{array}\right|$
$\Rightarrow 2 \times 5-3 \times 4=x \times 5-3 \times 2 x$
$\Rightarrow 10-12=5 x-6 x$
$\Rightarrow-2=-x$
$\Rightarrow x=2$
Standard 12
Mathematics