Could you give me please some tips or direction on how should I deal with the following problem?
$A = \left( a_{i,j} \right)$ is a Matrix from $M(n\times n, \mathbb{R})$ so that for all $ i\in \left \{ 1,\ldots,n \right \}$ exists $j$ such that:
$\left|a_{i,j}\right|>\left|a_{i,1}\right|+\left|a_{i,2}\right|+\ldots+\left| a_{i,i-1}\right|+\left|a_{i,i+1}\right|+ \cdots +\left | a_{i,n} \right|.$
I have to prove, that $\operatorname{rank}\left ( A \right ) = n$.
Thank you in advance.