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Home  >>  CBSE XII  >>  Math  >>  Determinants
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Find the values of $x$, if $ \text{: } \begin{vmatrix} 2&3 \\ 4&5 \end{vmatrix} = \begin{vmatrix} x&3 \\ 2x&5 \end{vmatrix}$

Note: This is part 2 of a 2 part question, split as 2 separate questions here.
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  • A determinant of order $2\times 2$ can be evaluated as $\begin{vmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{vmatrix}$
  • $\mid A\mid=a_{11}a_{22}-a_{21}a_{12}$
Find the values of x if
(ii)$\begin{vmatrix}2 & 3\\4 & 5\end{vmatrix}=\begin{vmatrix}x &3\\2x & 5\end{vmatrix}$
We know the value of determinant of order $2\times 2$ is $(a_{11}a_{22}-a_{21}a_{12})$
Hence LHS=$2\times 5-3\times 4$
RHS=$x\times 5-3\times 2x$
Now equating the both,
$\Rightarrow x=2.$


answered Mar 6, 2013 by sreemathi.v
edited Mar 6, 2013 by vijayalakshmi_ramakrishnans

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