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.