Chapter 2.5B, Problem 4GCE

To determine

To find: the equations represented by the reduced row echelon form of the matrix and state its relation with the original system.

Answer to Problem 4GCE

The systems of equation for reduced row echelon form are shown below.

  $\begin{array}{rrrrr}\hfill \begin{array}{l}rref\left(A\right)\\ x=-1\\ y=5\\ z=-2\end{array}& \hfill & \hfill \begin{array}{l}rref\left(B\right)\\ x=7\\ y=1\\ z=-2\end{array}& \hfill & \hfill \begin{array}{l}rref\left(C\right)\\ w=1\\ x=-1\\ y=2\\ z=-2\end{array}\end{array}$

The system of equation for the reduced row echelon matrix gives the solutions to the original system of equation.

Explanation of Solution

Given information:

Calculation:

The system of equations for $rref\left(A\right)$ matrix can be rewritten as follows:

  $\begin{array}{c}x=-1\\ y=5\\ z=-2\end{array}$

The system of equations for $rref\left(B\right)$ matrix can be rewritten as follows:

  $\begin{array}{c}x=7\\ y=1\\ z=-2\end{array}$

The system of equations for $rref\left(B\right)$ matrix can be rewritten as follows:

  $\begin{array}{c}w=1\\ x=-1\\ y=2\\ z=-2\end{array}$

The system of equation for the reduced row echelon matrix gives the solutions to the original system of equation.