Chapter A.2, Problem 1P

In each case, reduce $A$ to row reduce echelon form and determine $\text{rank}(A)$.

(a) $A=\left(\begin{array}{ccc}1& -3& 4\\ 2& -6& 8\end{array}\right)$

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

(c) $A=\left(\begin{array}{ccc}1& 2& 1\\ 2& -1& 3\\ 1& -5& 3\end{array}\right)$

(d) $A=\left(\begin{array}{cccc}1& 0& -2& -1\\ -1& 1& 1& 0\\ 1& 1& -3& -2\\ 2& -3& -1& 1\end{array}\right)$