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Home  >>  CBSE XII  >>  Math  >>  Determinants
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$ \text{If } \begin{vmatrix} x&2 \\ 18&x \end{vmatrix} = \begin{vmatrix} 6&2 \\ 18&6 \end{vmatrix}$, then $x$ is equal to:

$\begin{array}{1 1} 6 \\ \pm 6 \\ -6 \\ 0 \end{array} $

Can you answer this question?
 
 

1 Answer

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Toolbox:
  • A determinant of order $2\times 2$ can be evaluated as $\begin{vmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{vmatrix}$
  • $\mid A\mid=a_{11}a_{22}-a_{21}a_{12}$
If $\begin{vmatrix}x & 2\\18 & x\end{vmatrix}=\begin{vmatrix}6 &2\\18 & 6\end{vmatrix}$
 
then x is
 
We know the value of determinant of order $2\times 2$ is $(a_{11}a_{22}-a_{21}a_{12})$
 
Hence LHS=$x^2-(18\times 2)$
 
$\qquad\qquad=x^2-36$
 
$RHS=6\times 6-18\times 2$
 
$\qquad=36-36=0$
 
Equating LHS and RHS
 
$x^2-36=0$
 
$x^2=36$
 
$x=\pm 6$
 
Hence the correct answer is B.

 

answered Feb 20, 2013 by sreemathi.v
 

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