31. X1 3x3 = -2 - 3x, + X2 2x3 %D - 2x, + 2x, + X3 : 4 %3D
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 using either Gaussian elimination with back-substitution or Gauss-Jordan elimination
![Transcription of Systems of Equations:
**31.**
\[
\begin{align*}
x_1 - 3x_3 &= -2 \\
3x_1 + x_2 - 2x_3 &= 5 \\
2x_1 + 2x_2 + x_3 &= 4 \\
\end{align*}
\]
**32.**
\[
\begin{align*}
3x_1 - 2x_2 + 3x_3 &= 22 \\
3x_2 - x_3 &= 24 \\
6x_1 - 7x_2 &= -22 \\
\end{align*}
\]
**33.**
\[
\begin{align*}
2x_1 + x_2 + 3x_3 &= 3 \\
4x_1 - 3x_2 + 7x_3 &= 5 \\
8x_1 - 9x_2 + 15x_3 &= 10 \\
\end{align*}
\]
**34.**
\[
\begin{align*}
x_1 + x_2 - 5x_3 &= 3 \\
x_1 - 2x_3 &= 1 \\
2x_1 - x_2 - x_3 &= 0 \\
\end{align*}
\]
**35.**
\[
\begin{align*}
4x + 12y - 7z - 20w &= 22 \\
3x + 9y - 5z - 28w &= 30 \\
\end{align*}
\]
**36.**
\[
\begin{align*}
x + 2y + z &= 8 \\
-3x - 6y - 3z &= -21 \\
\end{align*}
\]
These systems of equations consist of multiple linear equations with variables \(x_1, x_2, x_3\), \(x, y, z,\) and \(w\). Each system represents a different mathematical problem to solve for the values of the variables involved.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c6e41b2-48f8-48f8-9e99-525c35ddf3fa%2Ffb4adbb2-4bef-4a19-a3cf-dfb5a97f2ae9%2Fo0rw3up_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Transcription of Systems of Equations:
**31.**
\[
\begin{align*}
x_1 - 3x_3 &= -2 \\
3x_1 + x_2 - 2x_3 &= 5 \\
2x_1 + 2x_2 + x_3 &= 4 \\
\end{align*}
\]
**32.**
\[
\begin{align*}
3x_1 - 2x_2 + 3x_3 &= 22 \\
3x_2 - x_3 &= 24 \\
6x_1 - 7x_2 &= -22 \\
\end{align*}
\]
**33.**
\[
\begin{align*}
2x_1 + x_2 + 3x_3 &= 3 \\
4x_1 - 3x_2 + 7x_3 &= 5 \\
8x_1 - 9x_2 + 15x_3 &= 10 \\
\end{align*}
\]
**34.**
\[
\begin{align*}
x_1 + x_2 - 5x_3 &= 3 \\
x_1 - 2x_3 &= 1 \\
2x_1 - x_2 - x_3 &= 0 \\
\end{align*}
\]
**35.**
\[
\begin{align*}
4x + 12y - 7z - 20w &= 22 \\
3x + 9y - 5z - 28w &= 30 \\
\end{align*}
\]
**36.**
\[
\begin{align*}
x + 2y + z &= 8 \\
-3x - 6y - 3z &= -21 \\
\end{align*}
\]
These systems of equations consist of multiple linear equations with variables \(x_1, x_2, x_3\), \(x, y, z,\) and \(w\). Each system represents a different mathematical problem to solve for the values of the variables involved.
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