Q : 7         Find values of x, if

                 (ii)  \begin{vmatrix}2 &3 \\ 4 &5 \end{vmatrix}=\begin{vmatrix}x &3 \\2x &5 \end{vmatrix}

Answers (1)

Given  \begin{vmatrix}2 &3 \\ 4 &5 \end{vmatrix}=\begin{vmatrix}x &3 \\2x &5 \end{vmatrix};

So, we here equate both sides after calculating each side's determinant values.

L.H.S. determinant value;

\dpi{100} \begin{vmatrix}2 &3 \\ 4 &5 \end{vmatrix}= 10 - 12 = -2

Similarly R.H.S. determinant value;

\begin{vmatrix}x &3 \\2x &5 \end{vmatrix} = 5(x) - 3(2x) = 5x - 6x =-x

So, we have then;

-2 = -x    or    x =2.

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