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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 55 (page 730)

In Problems 37鈥�72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x - 2 y + 3 z = 6 \\ - x + 2 y + z = 5 \\ 3 x - 4 y - z = 1 \end{cases}$

Short Answer

Expert verified

The system of equation is inconsistent.

Step by step solution

01

Step 1. Given information.

The given system of equation are

$\{\begin{cases} 2 x - 2 y + 3 z = 6 \\ - x + 2 y + z = 5 \\ 3 x - 4 y - z = 1 \end{cases}$

02

Step 2. Calculation.

The augmented matrix of the system is:

$[\begin{matrix} \begin{matrix} 2 & - 2 & 3 \\ - 1 & 2 & z \\ 3 & - 4 & - 1 \end{matrix} & \begin{matrix} 6 \\ 5 \\ 1 \end{matrix} \end{matrix}]$

Perform the row operations $R_{2} = r_{2} - 2 r_{1}; R_{3} = r_{3} + r_{1}$ :

$[\begin{matrix} \begin{matrix} 2 & - 2 & 3 \\ 0 & 1 & - 4 \\ 0 & 1 & - 4 \end{matrix} & \begin{matrix} 6 \\ - 12 \\ 7 \end{matrix} \end{matrix}]$

Perform the row operations $R_{3} = r_{3} - r_{2}$ :

$[\begin{matrix} \begin{matrix} 2 & - 2 & 3 \\ 0 & 1 & - 4 \\ 0 & 0 & 0 \end{matrix} & \begin{matrix} 6 \\ - 12 \\ 19 \end{matrix} \end{matrix}]$

Use the obtained matrix to write the system of equations.

$2 x - 2 y + 3 z = 6 y - 4 z = - 12 0 = 19$

This system is impossible to solve. Therefore, this system of equation is inconsistent.

03

Step 3. Conclusion.

The system of equation is inconsistent.

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Most popular questions from this chapter

Graph each inequality by hand.

$3 x + 2 y 鈮� 6$

solve each system of equations. If the system has no solution, say that it is inconsistent.

$2 x - 2 y + 3 z = 6 4 x - 3 y + 2 z = 0 - 2 x + 3 y - 7 z = 1$

The perimeter of a rectangle is $16$ inches, and its area is $15 i n c h e s^{2}$ . What are its dimensions?

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\{\begin{matrix} x + 2 y = 4 \\ 2 x + 4 y = 8 \end{matrix}$

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} + 1 \\ y = 4 x + 1 \end{cases}$

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