Chapter 4.6, Problem 4E

To determine

To evaluate: an augmented matrix for system of equations and solve by graphing calculator.

Answer to Problem 4E

The solution is $\left(0.75,-0.5\right)$

Explanation of Solution

Given information:

  $\begin{array}{l}4x+6y=0\\ 8x-2y=7\end{array}$ .

Formula used:

An augmented matrix contains the coefficient matrix of an extra column containing the constant terms.

Calculation:

Step 1.

Using system of equations the augmented matrix is ,

  $\begin{array}{l}4x+6y=0\\ 8x-2y=7\end{array}$

  $A=\left[\begin{array}{l}\begin{array}{ccc}4& 6& 0\end{array}\\ \begin{array}{ccc}8& -2& 7\end{array}\end{array}\right]$

Keystrokes:

  $\begin{array}{l}\boxed{2nd}[MATRIX]\boxed{⊳}\boxed{⊳}\boxed{ENTER}2\boxed{ENTER}3\boxed{ENTER}\\ 4\boxed{ENTER}6\boxed{ENTER}0\boxed{ENTER}\\ 8\boxed{ENTER}(-)2\boxed{ENTER}7\boxed{ENTER}\end{array}$

Step 2.

The reduced row echelon form (rref) using the graphing calculator.

Keystrokes:

  $\boxed{2nd}[QUIT]\boxed{2nd}[MATRIX]\boxed{⊳}\boxed{ALPHA}[A][MATRIX]\boxed{ENTER}\boxed{)}\boxed{ENTER}$

The first two columns are same as $2\times 2$ identity matrix. The first two row represents

  $x=0.75$ , the second row represents $y=-0.5$ . The solution is

  $\left(4,-6\right)$ .

  

Hence, the solution is $\left(0.75,-0.5\right)$ .