Does a matrix such as:
$ \begin{pmatrix} a & b\\ c & d\\ e & f \end{pmatrix} $
Which is a $3\times 2$ matrix span the third dimension if possible. I know its homegenious equation as infinite solutions but.... thats not being intuitive. I wanted to know this to clarify my view on onto transformations.
Recall that in general to span $\mathbb{R^n}$ we need at least n (independent) vectors therefore the columns of the given matrix span
a plane if they are linearly independent, that is rank(A)=2
line if they are not linearly independent, that is rank(A)=1