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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. 56 (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.
$\{\begin{cases} 3 x - 2 y + 2 z = 6 \\ 7 x - 3 y + 2 z = - 1 \\ 2 x - 3 y + 4 z = 0 \end{cases}$

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

$\{\begin{cases} 3 x - 2 y + 2 z = 6 \\ 7 x - 3 y + 2 z = - 1 \\ 2 x - 3 y + 4 z = 0 \end{cases}$

02

Step 2. Calculation.

The augmented matrix of the system is:

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

Perform the row operations $R_{2} = 3 r_{2} - 7 r_{1}, R_{3} = 3 r_{3} - 2 r_{1}$ :

$[\begin{matrix} \begin{matrix} 3 & - 2 & 2 \\ 0 & 5 & - 8 \\ 0 & - 5 & 8 \end{matrix} & \begin{matrix} 6 \\ - 45 \\ 12 \end{matrix} \end{matrix}]$

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

$[\begin{matrix} \begin{matrix} 3 & - 2 & 2 \\ 0 & 5 & - 8 \\ 0 & 0 & 0 \end{matrix} & \begin{matrix} 6 \\ - 45 \\ - 57 \end{matrix} \end{matrix}]$

Use the obtained matrix to write the system of equations.

$3 x - 2 y + 2 z = 6 5 y - 8 z = - 45 0 = - 57$

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

Verify that the values of the variables listed are solutions of the system of equations.

$\{\begin{matrix} x - y = 3 \\ - 3 x + y = 1 \end{matrix} x = - 2, y = - 5; (- 2, - 5)$

Constructing a Box: A rectangular piece of cardboard, whose area is 216 square centimeters, is made into an open box by cutting a 2-centimeter square from each corner and turning up the sides. See the figure. If the box is to have a volume of 224 cubic centimeters, what size cardboard should you start with?

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

$y = 3 x - 5; x^{2} + y^{2} = 5$

Graph each inequality by hand.

$y 鈮� 2$

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

$2 x + y = 4 - 2 y + 4 z = 0 3 x - 2 z = - 11$

See all solutions

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