Column space of $$$\left[\begin{array}{c}-1\end{array}\right]$$$

Find the column space of $$$\left[\begin{array}{c}-1\end{array}\right]$$$.

The reduced row echelon form of the matrix is $$$\left[\begin{array}{c}1\end{array}\right]$$$ (for steps, see rref calculator).

The column space is a space spanned by the columns of the initial matrix that correspond to the pivot columns of the reduced matrix.

Thus, the column space is $$$\left\{\left[\begin{array}{c}-1\end{array}\right]\right\}$$$.

The column space of the matrix is $$$\left\{\left[\begin{array}{c}-1\end{array}\right]\right\}$$$A.