Question

Given that M is a singular matrix, evaluate x where;

6 7 -1

M = 3 x 5

9 11 x

Answer 1

$M=\begin{pmatrix} 6& 7 & -1\\ 3 & x & 5\\ 9& 11 & x \end{pmatrix}$

det M=0

$\begin{vmatrix} 6& 7 & -1\\ 3 & x & 5\\ 9& 11 & x \end{vmatrix}=0\\ 6x^2-33+315+9x-330-21x=0\\ 6x^2-12x-48=0\\ x^2-2x-8=0\\ x_1=-2, x_2=4$