True or False:
Let $A$ be an $m\times n$ matrix. If $m
then $\dim(\ker(A)) > 0$ (i.e the dimension of the null space of is positive).
This is true? Because the $n$-$m$ extra columns are not linearly independent and can be constructed by some combination of the $m$ columns if those are independent and the null space will have dimension $n-m$?
Trying to get an intuitive handle on this stuff...