Chapter 8.1, Problem 62E

To determine

The system of linear equations.

Answer to Problem 62E

  $\boxed{\begin{array}{l}x=-6\\ y=10\end{array}}$

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.

  $\left[\begin{array}{cccc}1& 0& ⋮& -6\\ 0& 1& ⋮& 10\end{array}\right]$

Calculation:

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

We know the properties of reduced row- echelon form

1. Any rows consisting entirely of zeros occur at the bottom of the matrix.

2. For each row that does not consist entirely of zeros, the first nonzero entry is 1 (called a leading 1).

3. For two successive (nonzero) rows, the leading 1 in the higher row is farther to the left than the leading 1 in the lower row.

The given augmented matrix has two rows having two variables ( $x$ and $y$ ).

The matrix is in reduced row- echelon form.

Hence the value of variables is $\boxed{\begin{array}{l}x=-6\\ y=10\end{array}}$