Question

Generate a polynimial equation if $A$ is singular.

$A=\left[\begin{array}{ccc}x-1& 1& 1\\ 1& x-1& 1\\ 1& 1& x-1\end{array}\right]$

Answer 1

For matrix to be Singular its determinant must be $0$

$⟹|A|=0$

$\Rightarrow (x-1)(x^2-2x+1-1)-1(x-1-1)+1(1-x+1)=0$

$\Rightarrow x^3-2x^2-x^2+2x-x+2-x=0$

$\therefore x^3-3x^2+2=0$