Solve the system 5x1 -6x2 +4x3 +4x4 : +x2 +3x3 +3x4 4x1 -5x2 +7x3 +7x4 = 2x1 -2x2 -6x3 -6x4 1 3 -2 +s +t x3
Solve the system 5x1 -6x2 +4x3 +4x4 : +x2 +3x3 +3x4 4x1 -5x2 +7x3 +7x4 = 2x1 -2x2 -6x3 -6x4 1 3 -2 +s +t x3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Solve the system**
Given the system of linear equations:
\[
\begin{cases}
5x_1 - 6x_2 + 4x_3 + 4x_4 = 2 \\
-x_1 + x_2 + 3x_3 + 3x_4 = 1 \\
4x_1 - 5x_2 + 7x_3 + 7x_4 = 3 \\
2x_1 - 2x_2 - 6x_3 - 6x_4 = -2
\end{cases}
\]
Express the solution for the variables \(x_1\), \(x_2\), \(x_3\), and \(x_4\) in terms of parameters \(s\) and \(t\):
\[
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
x_4
\end{bmatrix}
=
\begin{bmatrix}
\\
\\
\\
\end{bmatrix}
+
s \begin{bmatrix}
\\
\\
\\
\end{bmatrix}
+
t \begin{bmatrix}
\\
\\
\\
\end{bmatrix}
.
\]
Please proceed to solve this system using appropriate techniques such as Gaussian elimination, substitution, or matrix methods to find the expressions for each variable in terms of \(s\) and \(t\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70a05657-0307-4b7c-962c-ab3824846297%2F928db799-8529-4365-80e9-bc0a9b93222e%2Fa4bcmie_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve the system**
Given the system of linear equations:
\[
\begin{cases}
5x_1 - 6x_2 + 4x_3 + 4x_4 = 2 \\
-x_1 + x_2 + 3x_3 + 3x_4 = 1 \\
4x_1 - 5x_2 + 7x_3 + 7x_4 = 3 \\
2x_1 - 2x_2 - 6x_3 - 6x_4 = -2
\end{cases}
\]
Express the solution for the variables \(x_1\), \(x_2\), \(x_3\), and \(x_4\) in terms of parameters \(s\) and \(t\):
\[
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
x_4
\end{bmatrix}
=
\begin{bmatrix}
\\
\\
\\
\end{bmatrix}
+
s \begin{bmatrix}
\\
\\
\\
\end{bmatrix}
+
t \begin{bmatrix}
\\
\\
\\
\end{bmatrix}
.
\]
Please proceed to solve this system using appropriate techniques such as Gaussian elimination, substitution, or matrix methods to find the expressions for each variable in terms of \(s\) and \(t\).
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