Let $\displaystyle L : R^4 \rightarrow R^3$ be defined by $\displaystyle L(x,y,z,w)=(x+y,z+w,x+z)$ Find a basis for range L.

What I did:

$\displaystyle {

\left[\begin{array}{c}1\\0\\1\end{array}\right]

\left[\begin{array}{c}1\\0\\0\end{array}\right]

\left[\begin{array}{c}0\\1\\1\end{array}\right]

\left[\begin{array}{c}0\\1\\0\end{array}\right]

}$ spans range L

but rref of the coefficent matrix has a row of zeros so it's not a spanning set.