Question

If \[\begin{vmatrix}x + 1 & x - 1 \\ x - 3 & x + 2\end{vmatrix} = \begin{vmatrix}4 & - 1 \\ 1 & 3\end{vmatrix}\], then write the value of x.

Answer 1

\[\begin{vmatrix}x + 1 & x - 1 \\ x - 3 & x + 2\end{vmatrix} = \begin{vmatrix}4 & - 1 \\ 1 & 3\end{vmatrix}\] 
\[ \Rightarrow \left( x + 1 \right)\left( x + 2 \right) - \left( x - 1 \right)\left( x - 3 \right) = 12 + 1\] 
\[ \Rightarrow x^2 + 3x + 2 - x^2 + 4x - 3 = 13\] 
\[ \Rightarrow 7x - 1 = 13\] 
\[ \Rightarrow 7x = 14\] 
\[ \Rightarrow x = 2\] 
Hence, the value of x is 2 .