College Algebra, Chapter 7, 7.1, Section 7.1, Problem 4

Find the solution of the system to the reduced row-echelon form of augmented matrix of a system or linear equations.

a.) $\left[ \begin{array}{cccc}
1 & 0 & 0 & 2 \\
0 & 1 & 0 & 1 \\
0 & 0 & 1 & 3
\end{array} \right]$


$
\begin{equation}
\begin{aligned}

x =& \underline{2}
\\
y =& \underline{1}
\\
z =& 3

\end{aligned}
\end{equation}
$


b.) $\left[ \begin{array}{cccc}
1 & 0 & 1 & 2 \\
0 & 1 & 1 & 1 \\
0 & 0 & 0 & 0
\end{array} \right]$


$
\begin{equation}
\begin{aligned}

x =& \underline{2 - t}
\\
y =& \underline{1 - t}
\\
z =& \underline{t}

\end{aligned}
\end{equation}
$


c.) $\left[ \begin{array}{cccc}
1 & 0 & 0 & 2 \\
0 & 1 & 0 & 1 \\
0 & 0 & 0 & 3
\end{array} \right]$

The system has no solution.