This is a question that has stumped me. It asks "Without computing A, find bases for the four fundamental subspaces." The $LU$ equation is as follows:
$\begin{bmatrix} 1 & 0 & 0 \\ 6 & 1 & 0 \\ 9 & 8 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 1 & 2 \end{bmatrix}$
I understand that $N(A) = \begin{bmatrix} 0 \\ 2 \\ -1 \\ 1 \end{bmatrix} $ and that there is no $N(A^T)$ because there are no zero rows in $U$, but I do not know what to do for the column/row spaces without computing $A$. I could compute columns 1, 2, and 3 because it's not "$A$" but I know that's not what they want.