Question

For what value of x the matrix A is singular? 
\[ A = \begin{bmatrix}1 + x & 7 \\ 3 - x & 8\end{bmatrix}\]

Answer 1

Matrix A will be singular if  [ A ] = 0

\[\left| A \right| = \begin{vmatrix}1 + x & 7 \\ 3 - x & 8\end{vmatrix} = 0\]
\[ \Rightarrow 8 + 8x - 21 + 7x = 0\]
\[ \Rightarrow 15x - 13 = 0\]
\[ \Rightarrow 15x = 13\]
\[ \Rightarrow x = \frac{13}{15}\]