Chapter 1.2, Problem 1E

Which of the matrices that follow are in row echelon form? Which are in reduced row echelon form?

(a) $\left(\begin{array}{cc}1& 2\\ 0& 0\end{array}\begin{array}{cc}3& 4\\ 1& 2\end{array}\right)$

(b) $\left(\begin{array}{ccc}1& 0& 0\\ 0& 0& 0\\ 0& 0& 1\end{array}\right)$

(c) $\left(\begin{array}{ccc}1& 3& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right)$

(d) $\left(\begin{array}{c}0\\ 0\\ 0\end{array}\begin{array}{c}1\\ 0\\ 0\end{array}\right)$

(e) $\left(\begin{array}{ccc}1& 1& 1\\ 0& 1& 2\\ 0& 0& 3\end{array}\right)$

(f) $\left(\begin{array}{ccc}1& 4& 6\\ 0& 0& 1\\ 0& 0& 3\end{array}\right)$

(g) $\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\begin{array}{ccc}1& 1& 2\\ 2& 2& 5\\ 3& 3& 6\end{array}\right)$

(h) $\left(\begin{array}{ccc}1& 1& 3\\ 0& 0& 1\\ 0& 0& 0\end{array}\begin{array}{c}4\\ 3\\ 0\end{array}\right)$