Let we have the following matrix:
$$ \begin{matrix} 1 & \alpha & 0 \\ \beta & 1 & 1 \\ 0 & 1 & 1 \\ \end{matrix} $$
Is the matrix $A$ strictly diagonally dominant? Or better said, for which values of $\alpha$ and $\beta$ is the matrix $A$ strictly diagonally dominant?
I know that a matrix is strictly dominant if $|a_{ii}|>\sum_{j=1,j\neq{i}}^n |a_{ij}|$
So we've got the following:
$|a_{11}|=1>\alpha + 0=\alpha$ ; So the first condition is that $\alpha>1$
$|a_{22}|=1>|\beta| + 1$ ; But it is impossible to be $|\beta|<0$
$|a_{33}|=1>0 + 1=1$ ; And also, $1$ is not bigger than $1$...
So isn't it possible for A to be strictly diagonally dominant?