Chapter 7.4, Problem 33E

To determine

To solve the augmented matrix using graphing utility.

Answer to Problem 33E

The solution of the system of linear equation is $x=-2$ and $y=4$ .

Explanation of Solution

Given information:

The augmented matrix is given as:

  $\left[\begin{array}{cccc}-3& 4& ⋮& 22\\ 6& -4& ⋮& -28\end{array}\right]$

Calculation:

The solution of the system of linear equation using graphing utility is obtained as:

1. Enter the matrix by using the combination of keystrokes $\boxed{\text{2nd}}+\boxed{x^{-1}}$
2. Use cursor key to select the edit option and then select row 1 of matrix A and press $\boxed{\text{Enter}}$ .
3. Enter the dimension of the matrix (3 rows by 4 columns).
4. Enter the values of the coefficient matrix (row by row).
5. Go to Matrix again by pressing $\boxed{\text{2nd}}+\boxed{x^{-1}}$
6. Select the MATH option.
7. Select the option rref(and press $\boxed{\text{Enter}}$ .
8. Go to matrix again, choose [A]
9. Press $\boxed{\text{Enter}}$ to see the reduced augmented matrix.

The reduced augmented matrix is displayed as:

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

The matrix is in row-echelon form, and the corresponding system is,

  $\{\begin{array}{c}3x=-6\\ -4y=-16\end{array}$

Hence,

The solution of the system of linear equation is $x=-2$ and $y=4$ .