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
![The image is an educational exercise that demonstrates how to write a system of linear equations in matrix form.
---
**Problem Statement:**
Write the system of linear equations as a matrix equation.
**Given Equations:**
1. \(12x - 8y + 9z = -8\)
2. \(-3x - 5y + 12 = -7\)
3. \(8x - 2y - 2z = 9\)
---
**Matrix Representation:**
The system can be represented in the form \(AX = B\), where:
**Matrix \(A\):**
\[
\begin{bmatrix}
12 & -8 & 9 \\
-3 & -5 & 12 \\
8 & -2 & -2
\end{bmatrix}
\]
**Matrix \(X\):**
\[
\begin{bmatrix}
x \\
y \\
z
\end{bmatrix}
\]
**Matrix \(B\):**
\[
\begin{bmatrix}
-8 \\
-7 \\
9
\end{bmatrix}
\]
This matrix equation represents the system of linear equations compactly.
**Explanation of Diagram Elements:**
- The three matrices are shown in separate, colored boxes: \(A\) in a green box, \(X\) in a neutral box, and \(B\) in a red box.
- The goal is to express the linear equations in matrix form, making the system easier to analyze and solve using matrix operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc167378a-6772-4355-bdb0-a5fec1af8d0e%2Fd32c8c1a-eeea-4c89-9d52-7334d08a2328%2Fei1ndr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image is an educational exercise that demonstrates how to write a system of linear equations in matrix form.
---
**Problem Statement:**
Write the system of linear equations as a matrix equation.
**Given Equations:**
1. \(12x - 8y + 9z = -8\)
2. \(-3x - 5y + 12 = -7\)
3. \(8x - 2y - 2z = 9\)
---
**Matrix Representation:**
The system can be represented in the form \(AX = B\), where:
**Matrix \(A\):**
\[
\begin{bmatrix}
12 & -8 & 9 \\
-3 & -5 & 12 \\
8 & -2 & -2
\end{bmatrix}
\]
**Matrix \(X\):**
\[
\begin{bmatrix}
x \\
y \\
z
\end{bmatrix}
\]
**Matrix \(B\):**
\[
\begin{bmatrix}
-8 \\
-7 \\
9
\end{bmatrix}
\]
This matrix equation represents the system of linear equations compactly.
**Explanation of Diagram Elements:**
- The three matrices are shown in separate, colored boxes: \(A\) in a green box, \(X\) in a neutral box, and \(B\) in a red box.
- The goal is to express the linear equations in matrix form, making the system easier to analyze and solve using matrix operations.
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