Chapter 11: Q. 51 (page 730)

In Problems 37–72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x - 2 y - 2 z = 2 \\ 2 x + 3 y + z = 2 \\ 3 x + 2 y = 0 \end{cases}$

Short Answer

Expert verified

The system of equation is inconsistent.

Step by step solution

Step 1. Given information.

The given system of equation are

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

Step 2. Calculation.

The augmented matrix of the system is:

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

Perform the row operations $R_{1} = \frac{1}{2} r_{1}$ :

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

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

$[\begin{matrix} \begin{matrix} 1 & - 1 & - 1 \\ 0 & 5 & 3 \\ 0 & 5 & 3 \end{matrix} & \begin{matrix} 1 \\ 0 \\ - 3 \end{matrix} \end{matrix}]$

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

$[\begin{matrix} \begin{matrix} 1 & - 1 & - 1 \\ 0 & 5 & 3 \\ 0 & 0 & 0 \end{matrix} & \begin{matrix} 1 \\ 0 \\ - 3 \end{matrix} \end{matrix}]$

Use the obtained matrix to write the system of equations.

$x - y - z = 1 5 y + 3 z = 0 0 = - 3$

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

Step 3. Conclusion.

The system of equation is inconsistent.

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In Problems 37–72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x - 2 y - 2 z = 2 \\ 2 x + 3 y + z = 2 \\ 3 x + 2 y = 0 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

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In Problems 37–72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.2x-2y-2z=22x+3y+z=23x+2y=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Statistics

Calculus

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 37–72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x - 2 y - 2 z = 2 \\ 2 x + 3 y + z = 2 \\ 3 x + 2 y = 0 \end{cases}$