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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Question
![**Problem Statement:**
Find the augmented matrix of the linear system.
**Given:**
\( a - 6b + \, \, \, \, \, \, \, \, \, \, \, d = 5 \)
\(-a + b - c - 8d = 1 \)
**Augmented Matrix:**
The augmented matrix for this system is structured as:
\[
\begin{pmatrix}
1 & -6 & 0 & 1 & \vert & 5 \\
-1 & 1 & -1 & -8 & \vert & 1
\end{pmatrix}
\]
**Explanation:**
- The first equation, \( a - 6b + d = 5 \), corresponds to the first row of the matrix. For variable \( a \), there is a coefficient of 1; for \( b \), the coefficient is -6; for \( c \), it is 0 (as \( c \) does not appear in the equation); for \( d \), the coefficient is 1.
- The second equation, \(-a + b - c - 8d = 1 \), corresponds to the second row. Here, the coefficients are -1 for \( a \), 1 for \( b \), -1 for \( c \), and -8 for \( d \).
- The vertical line separates the coefficients of the variables from the constants on the right side of the equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6948d5d-782c-4f32-af22-abf47b4c3397%2F5987da8e-5e1e-4672-986e-65942f4bae25%2Fouaq6qu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the augmented matrix of the linear system.
**Given:**
\( a - 6b + \, \, \, \, \, \, \, \, \, \, \, d = 5 \)
\(-a + b - c - 8d = 1 \)
**Augmented Matrix:**
The augmented matrix for this system is structured as:
\[
\begin{pmatrix}
1 & -6 & 0 & 1 & \vert & 5 \\
-1 & 1 & -1 & -8 & \vert & 1
\end{pmatrix}
\]
**Explanation:**
- The first equation, \( a - 6b + d = 5 \), corresponds to the first row of the matrix. For variable \( a \), there is a coefficient of 1; for \( b \), the coefficient is -6; for \( c \), it is 0 (as \( c \) does not appear in the equation); for \( d \), the coefficient is 1.
- The second equation, \(-a + b - c - 8d = 1 \), corresponds to the second row. Here, the coefficients are -1 for \( a \), 1 for \( b \), -1 for \( c \), and -8 for \( d \).
- The vertical line separates the coefficients of the variables from the constants on the right side of the equations.
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