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 of Educational Content:**
**Title:** Writing the Augmented Matrix for a System of Linear Equations
**Instructions:**
Write the augmented matrix (with no row operations) for the system of linear equations below:
**System of Equations:**
1. \(9x + y - z = 4\)
2. \(4x - y = 1\)
3. \(x - z = 9\)
**Matrix Representation:**
To represent this system as an augmented matrix, we align the coefficients of \(x\), \(y\), and \(z\) from each equation into rows and add the constants as the last column. The matrix will have the following structure based on the equations provided:
\[
\begin{bmatrix}
9 & 1 & -1 & \vline & 4 \\
4 & -1 & 0 & \vline & 1 \\
1 & 0 & -1 & \vline & 9 \\
\end{bmatrix}
\]
**Arrangement Explanation:**
- The first row corresponds to the coefficients from the equation \(9x + y - z = 4\).
- The second row uses the coefficients from \(4x - y = 1\).
- The third row includes coefficients from \(x - z = 9\).
The vertical line in the matrix is used to separate the coefficients of the variables from the constants on the right-hand side of the equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F816a2da0-337a-48cf-ad05-f3feadb237d1%2Fba671c02-cca9-45ed-a5e6-3268978e6bf6%2Fpx0fqas_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription of Educational Content:**
**Title:** Writing the Augmented Matrix for a System of Linear Equations
**Instructions:**
Write the augmented matrix (with no row operations) for the system of linear equations below:
**System of Equations:**
1. \(9x + y - z = 4\)
2. \(4x - y = 1\)
3. \(x - z = 9\)
**Matrix Representation:**
To represent this system as an augmented matrix, we align the coefficients of \(x\), \(y\), and \(z\) from each equation into rows and add the constants as the last column. The matrix will have the following structure based on the equations provided:
\[
\begin{bmatrix}
9 & 1 & -1 & \vline & 4 \\
4 & -1 & 0 & \vline & 1 \\
1 & 0 & -1 & \vline & 9 \\
\end{bmatrix}
\]
**Arrangement Explanation:**
- The first row corresponds to the coefficients from the equation \(9x + y - z = 4\).
- The second row uses the coefficients from \(4x - y = 1\).
- The third row includes coefficients from \(x - z = 9\).
The vertical line in the matrix is used to separate the coefficients of the variables from the constants on the right-hand side of the equations.
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