Chapter 3.4, Problem 16E

In Exercises $11-16$:

$a)$ Find a matrix $B$ in reduced echlon form such that $B$ is row equivalent to the given matrix $A$.

$b)$ Find a basis for the null space of $A$.

$c)$ As in Example $6$, find a basis for the range of $A$ that consists of columns of $A$. For each column, $A_j$, of $A$ that does not appear in the basis, express $A_j$ as a linear combination of the basis vectors.

$d)$ Exhibit a basis for the row space of $A$.

$A=\left[\begin{array}{ccc}2& 1& 2\\ 2& 2& 1\\ 2& 3& 0\end{array}\right]$