Chapter 8.2, Problem 27PE

(a)

To determine

To calculate: The system represented by the provided matrix $A=\left[\begin{array}{ccccc}1& 2& 5& 5& -3\\ 1& 1& 3& 4& -1\\ 1& -1& -1& 2& 3\end{array}\right]$ and $\text{rref}\left(\left[A\right]\right)=\left[\begin{array}{ccccc}1& 0& 1& 3& 1\\ 0& 1& 2& 1& -2\\ 0& 0& 0& 0& 0\end{array}\right]$.

(b)

To determine

To calculate: The solution by use of the reduced row echelon form for the provided matrix $A=\left[\begin{array}{ccccc}1& 2& 5& 5& -3\\ 1& 1& 3& 4& -1\\ 1& -1& -1& 2& 3\end{array}\right]$ and $\text{rref}\left(\left[A\right]\right)=\left[\begin{array}{ccccc}1& 0& 1& 3& 1\\ 0& 1& 2& 1& -2\\ 0& 0& 0& 0& 0\end{array}\right]$.