Question

If the matrix \[\begin{bmatrix}5x & 2 \\ - 10 & 1\end{bmatrix}\]  is singular, find the value of x.

Answer 1

A  matrix is said to be singular if its determinant is zero. Since the given matrix is singular, we get 
\[A = \begin{bmatrix} 5x & 2 \\- 10 & 1 \end{bmatrix} \] 
\[ \Rightarrow \left| A \right| = \begin{vmatrix} 5x & 2 \\- 10 & 1 \end{vmatrix} = 0\] 
\[ \Rightarrow 5x + 20 = 0 \left[\text{ Expanding }\right]\] 
\[ \Rightarrow x = - \frac{20}{5} = - 4\]