Solve the linear system X1 + x₂ + x3 + x4 = 1 3x₁ + x₂ + x3 x4 = 5 5x₁ - x2 + x3 - 5x4 = 3 Describe the solution set geometrically.
Solve the linear system X1 + x₂ + x3 + x4 = 1 3x₁ + x₂ + x3 x4 = 5 5x₁ - x2 + x3 - 5x4 = 3 Describe the solution set geometrically.
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
![**Problem 1**: Solve the linear system
\[
\begin{align*}
x_1 + x_2 + x_3 + x_4 &= 1 \\
3x_1 + x_2 + x_3 - x_4 &= 5 \\
5x_1 - x_2 + x_3 - 5x_4 &= 3
\end{align*}
\]
**Task**: Describe the solution set geometrically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ebe91de-3090-46ac-907f-d0393c4d1db8%2F090c13cc-6eed-4786-8589-dfade22aa280%2Fadc23zf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 1**: Solve the linear system
\[
\begin{align*}
x_1 + x_2 + x_3 + x_4 &= 1 \\
3x_1 + x_2 + x_3 - x_4 &= 5 \\
5x_1 - x_2 + x_3 - 5x_4 &= 3
\end{align*}
\]
**Task**: Describe the solution set geometrically.
Expert Solution

Step 1
The augmented matrix for given system of equations is
Apply the row operators
Apply
Apply
This is row reduced echelon (RREF) form of the matrix AB. Since number of equations(3) is less than to number of variables(4) so the system has infinite number of solutions.
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