Chapter 3.6, Problem 15E

Let A be a $4\times 5$ matrix and let U be the reduced row echelon form of A. If
${\text{a}}_{\text{1}}=\left(\begin{array}{c}2\\ 1\\ -3\\ -2\end{array}\right),{\text{a}}_{\text{2}}=\left(\begin{array}{l}-1\\ 2\\ 3\\ 1\end{array}\right),U=\left(\begin{array}{ccccc}1& 0& 2& 0& -1\\ 0& 1& 3& 0& -2\\ 0& 0& 0& 1& 5\\ 0& 0& 0& 0& 0\end{array}\right)$
a) find a basis for N(A).
b) given that ${\text{x}}_{\text{0}}$ is a solution to $A\text{x}=\text{b}$ where
$\text{b}=\left(\begin{array}{l}0\\ 5\\ 3\\ 4\end{array}\right)$ and ${\text{x}}_0=\left(\begin{array}{l}3\\ 2\\ 0\\ 2\\ 0\end{array}\right)$
(i) find all solutions to the system.
(ii) determine the remaining column vectors of A.