Let, $\displaystyle \ T =
\[\begin{bmatrix}
1 & 3 & -7 \\
2 & -1 & 0 \\
3 & -1 & -1\\
4 & -3 & -2
\end{bmatrix}
\] $
determine a basis for the (a) range space of $\displaystyle T $ and (b) null space of $\displaystyle T $
This is a subject of Linear Algebra.