Chapter 8.1, Problem 63E

To determine

The system of linear equations.

Answer to Problem 63E

  $\boxed{\begin{array}{l}x=-4\\ y=-10\\ z=4\end{array}}$

Explanation of Solution

Given information:

An augmented matrix that represents a system of linear equations (in variables and if applicable) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix.

  $\left[\begin{array}{ccccc}1& 0& 0& ⋮& -4\\ 0& 1& 0& ⋮& -10\\ 0& 0& 1& ⋮& 4\end{array}\right]$

Calculation:

The given matrix be reduced by applying using Gauss-Jordan elimination method. This method reduces the matrix by using row operation on it.

We know that augmented matrix has coefficients and constant terms both.

So that the system of linear equations be represented by augmented matrix is,

  $\{\begin{array}{l}1x+0y+0z=-4\\ 0x+1y+0z=-10\\ 0x+0y+1z=4\end{array}$

Now solve the variable in the given system of linear equations.

  $\begin{array}{l}x=-4\\ y=-10\\ z=4\end{array}$

Hence the values of variables is $\boxed{\begin{array}{l}x=-4\\ y=-10\\ z=4\end{array}}$