Chapter 7.3, Problem 30E

Solution

To identify: The system of equations corresponding to the augmented matrix.

  $\left[\begin{array}{ccccc}1& 0& -1& 2& -3\\ 2& 1& 0& -1& 4\\ -1& 1& 2& 0& 0\end{array}\right]$

The corresponding system of equation matrix.

  $\begin{array}{c}x-z+2w=-3\\ 2x+y-w=4\\ -x+y+2z=0\end{array}$

Given information:

The given augmented is.

  $\left[\begin{array}{ccccc}1& 0& -1& 2& -3\\ 2& 1& 0& -1& 4\\ -1& 1& 2& 0& 0\end{array}\right]$

Explanation:

Consider the given information.

To obtain the system of equation for the augmented matrix, first note that the last column lists the constants. The entries to the left of the constant are the coefficients of the variable. As used in this lesson, use the following variables in order $x,y,z\text{and}w$ .

So, the corresponding system of equation matrix is:

  $\begin{array}{c}x+0y-z+2w=-3\\ 2x+y+0z-w=4\\ -x+y+2z+0w=0\end{array}$

On Simplifying:

  $\begin{array}{c}x-z+2w=-3\\ 2x+y-w=4\\ -x+y+2z=0\end{array}$

Hence, the corresponding system of equation matrix.

  $\begin{array}{c}x-z+2w=-3\\ 2x+y-w=4\\ -x+y+2z=0\end{array}$