Question

for basis of null space. row space and column space, we must reduce to ref or rref?

Answer 1

rref for convenient.

Answer 2

You want to find out if the null space consists of only the zero vector \((0,0,0)\).
If it does then then solution is trivial.
If it's trivial, then it has no basis.

So you have to get the matrix into reduced row echelon form to see if it looks like this, for example.\[\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]=\left[\begin{matrix}0 \\ 0\end{matrix}\right]\]