Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Transcription for Educational Use**
The image presents a system of linear equations and its corresponding augmented matrix:
**System of Equations:**
\[
\begin{cases}
2x + 3y - z = -8 \\
x - y - z = -2 \\
-4x + 3y + z = 6 \\
\end{cases}
\]
**Augmented Matrix:**
\[
\begin{bmatrix}
2 & 3 & -1 & | & -8 \\
1 & -1 & -1 & | & -2 \\
-4 & 3 & 1 & | & 6 \\
\end{bmatrix}
\]
**Explanation:**
1. **Equations:** The system consists of three linear equations with three variables: \(x\), \(y\), and \(z\).
2. **Matrix Representation:** The augmented matrix is used to represent the system of equations compactly. Each row corresponds to an equation, with the coefficients of the variables and the constant on the right-hand side of the equation.
3. **Matrix Layout:**
- The first column represents the coefficients of \(x\).
- The second column represents the coefficients of \(y\).
- The third column represents the coefficients of \(z\).
- The vertical bar separates the coefficient matrix from the constants on the right-hand side of each equation.
At the right side of the image, there is a number "(9)" with a blank line next to it, but it is not directly connected to the matrix or system of equations provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F028128fd-b27f-44d7-985e-59cd58409734%2Fca74ff8a-7464-44a3-8a92-6a0096270a6b%2Fmjwzzk8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Use**
The image presents a system of linear equations and its corresponding augmented matrix:
**System of Equations:**
\[
\begin{cases}
2x + 3y - z = -8 \\
x - y - z = -2 \\
-4x + 3y + z = 6 \\
\end{cases}
\]
**Augmented Matrix:**
\[
\begin{bmatrix}
2 & 3 & -1 & | & -8 \\
1 & -1 & -1 & | & -2 \\
-4 & 3 & 1 & | & 6 \\
\end{bmatrix}
\]
**Explanation:**
1. **Equations:** The system consists of three linear equations with three variables: \(x\), \(y\), and \(z\).
2. **Matrix Representation:** The augmented matrix is used to represent the system of equations compactly. Each row corresponds to an equation, with the coefficients of the variables and the constant on the right-hand side of the equation.
3. **Matrix Layout:**
- The first column represents the coefficients of \(x\).
- The second column represents the coefficients of \(y\).
- The third column represents the coefficients of \(z\).
- The vertical bar separates the coefficient matrix from the constants on the right-hand side of each equation.
At the right side of the image, there is a number "(9)" with a blank line next to it, but it is not directly connected to the matrix or system of equations provided.
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