Question

For what value of x, the following matrix is singular?

\[\begin{bmatrix}5 - x & x + 1 \\ 2 & 4\end{bmatrix}\]

 

Answer 1

If a matrix A is singular, then  \[\left| A \right| = 0\]
\[\therefore \begin{vmatrix}5 - x & x + 1 \\ 2 & 4\end{vmatrix} = 0\]
\[\Rightarrow 4(5 - x) - 2(x + 1) 0\] 
\[ \Rightarrow 20 - 4x - 2x - 2\] 
\[ \Rightarrow 18 - 6x = 0\] 
\[ \Rightarrow 18 = 6x\] 
\[ \Rightarrow x = 3\]