Chapter 4.3, Problem 1MP

The matrices below are not in reduced form. Indicate which condition in the definition is violated for each matrix. State the row operation(s) required to transform the matrix into reduced form, and find the reduced form.

$\left(\text{A}\right)\left.\left[\left.\begin{array}{cc}1& 0\\ 0& 3\end{array}\right|\right.\begin{array}{c}2\\ -6\end{array}\right]\left(\text{B}\right)\left.\left[\left.\begin{array}{ccc}1& 5& 4\\ 0& 1& 2\\ 0& 0& 0\end{array}\right|\right.\begin{array}{c}3\\ -1\\ 0\end{array}\right]$

$\left(\text{C}\right)\left.\left[\left.\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right|\right.\begin{array}{c}-3\\ 0\\ 2\end{array}\right]\left(\text{D}\right)\left.\left[\left.\begin{array}{ccc}1& 2& 0\\ 0& 0& 0\\ 0& 0& 1\end{array}\right|\right.\begin{array}{c}3\\ 0\\ 4\end{array}\right]$