Browse Questions

# $\text{If } \begin{vmatrix} x&2 \\ 18&x \end{vmatrix} = \begin{vmatrix} 6&2 \\ 18&6 \end{vmatrix}$, then $x$ is equal to:

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

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.