Hello!!
Let $A$ be a $4\times 5$ matrix with rank $2$ and let $U$ be the corresponding row echelon form matrix.
I want to check if the following statement is true or not.
If $B$ is a $5\times 5$ invertible matrix, at least two of the columns of $B$ are not in the nulity of $A$.
Suppose that this false, then less than 2 columns of $B$ are not in the null space of $A$.Then at least 4 columns are in the null space.
What do we get from that?