4x - 3y + z = 0 4x-34 x+y -8x+6y-22=0 = 0 Z is arbitrary PPPP. Is there solution? solution set {(1,0,0) are there many solutions? Solution set & Da & no solution set
4x - 3y + z = 0 4x-34 x+y -8x+6y-22=0 = 0 Z is arbitrary PPPP. Is there solution? solution set {(1,0,0) are there many solutions? Solution set & Da & no solution set
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve the system. If the system has infinitely many solutions, write the solution set with z arbitrary. I keep writing my answers wrong and it gets kicked out.
![### System of Linear Equations
Consider the following system of equations:
1. \(4x - 3y + z = 0\)
2. \(x + y = 0\)
3. \(-8x + 6y - 2z = 0\)
### Analysis
- \(z\) is arbitrary.
### Solution Inquiry
- **Is there one solution?**
*Solution set*: \(\{[ \_\_\_, \_\_\_, \_\_\_ ]\}\)
- **Are there many solutions?**
*Solution set*: \(\{[ \_\_\_, \_\_\_, z ]\}\)
- **No solution set**: \(\emptyset\)
### Explanation
The equations given form a system that can be solved using methods of linear algebra. The arbitrary nature of \(z\) suggests that there may be infinitely many solutions, which can be expressed in terms of \(z\). Solving this system involves finding values for \(x\), \(y\), and \(z\) that satisfy all three equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb50150a-e50b-4a78-ab84-354e14945377%2F4aed80c7-d0ea-4310-b92b-1b7576ca1b83%2Fjzhtxov_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### System of Linear Equations
Consider the following system of equations:
1. \(4x - 3y + z = 0\)
2. \(x + y = 0\)
3. \(-8x + 6y - 2z = 0\)
### Analysis
- \(z\) is arbitrary.
### Solution Inquiry
- **Is there one solution?**
*Solution set*: \(\{[ \_\_\_, \_\_\_, \_\_\_ ]\}\)
- **Are there many solutions?**
*Solution set*: \(\{[ \_\_\_, \_\_\_, z ]\}\)
- **No solution set**: \(\emptyset\)
### Explanation
The equations given form a system that can be solved using methods of linear algebra. The arbitrary nature of \(z\) suggests that there may be infinitely many solutions, which can be expressed in terms of \(z\). Solving this system involves finding values for \(x\), \(y\), and \(z\) that satisfy all three equations.
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