Hi ! I'm been proving some theorems on linear algebra and I stumble upon one that I dont understand. It says if $A$ is a matrix m x n with $m < n$, then $AX = 0$ has at least one non trivial solution.
I get that if $m < n$, and if we name $r$ to the non null rows then $ r \le m$ then $ r < n$, and here it says as $ r < n $ we know it has at least one non trivial solution, why ? Is it because I have a variable dependent of the others ?