(a) X1 2x22x3 + 2x4 + 4x5 2x3 - 2x5 X4 2x5 - 0 0 (b) 3x1 9x1 6x1 x2 + 4x3 3x2 + 10x3 2x2 + 8x3 = - 0 0
(a) X1 2x22x3 + 2x4 + 4x5 2x3 - 2x5 X4 2x5 - 0 0 (b) 3x1 9x1 6x1 x2 + 4x3 3x2 + 10x3 2x2 + 8x3 = - 0 0
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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5. Write the solution set of the given homogeneous system in parametric vector form.
![### Systems of Linear Equations
Below are two sets of linear equations. Each set represents a system of equations that can be solved to find the values of the variables. These systems could be used in various mathematical applications such as linear algebra, differential equations, and modeling real-world scenarios.
#### (a) System of Equations
\[
\begin{cases}
x_1 - 2x_2 - 2x_3 + 2x_4 + 4x_5 = 0 \\
2x_3 - 2x_5 = 0 \\
x_4 - 2x_5 = 0
\end{cases}
\]
This system consists of three equations with five variables (\(x_1, x_2, x_3, x_4, x_5\)). To solve this system, methods such as substitution, elimination, or matrix operations (e.g., Gaussian elimination) can be applied.
#### (b) System of Equations
\[
\begin{cases}
3x_1 - x_2 + 4x_3 = 0 \\
9x_1 - 3x_2 + 10x_3 = 0 \\
6x_1 - 2x_2 + 8x_3 = 0
\end{cases}
\]
This system consists of three equations with three variables (\(x_1, x_2, x_3\)). Similar to system (a), this can be solved using various algebraic methods to find the values of the variables.
In educational settings, understanding how to solve these systems can be crucial for topics like vector spaces, transformations, or solving real-world problems modeled by linear relationships.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d07e113-70c7-44ea-a54a-4dad627b44c8%2F01fc91a3-f2fd-4556-9a68-e2b709a7e232%2F5mqh6jc_processed.png&w=3840&q=75)
Transcribed Image Text:### Systems of Linear Equations
Below are two sets of linear equations. Each set represents a system of equations that can be solved to find the values of the variables. These systems could be used in various mathematical applications such as linear algebra, differential equations, and modeling real-world scenarios.
#### (a) System of Equations
\[
\begin{cases}
x_1 - 2x_2 - 2x_3 + 2x_4 + 4x_5 = 0 \\
2x_3 - 2x_5 = 0 \\
x_4 - 2x_5 = 0
\end{cases}
\]
This system consists of three equations with five variables (\(x_1, x_2, x_3, x_4, x_5\)). To solve this system, methods such as substitution, elimination, or matrix operations (e.g., Gaussian elimination) can be applied.
#### (b) System of Equations
\[
\begin{cases}
3x_1 - x_2 + 4x_3 = 0 \\
9x_1 - 3x_2 + 10x_3 = 0 \\
6x_1 - 2x_2 + 8x_3 = 0
\end{cases}
\]
This system consists of three equations with three variables (\(x_1, x_2, x_3\)). Similar to system (a), this can be solved using various algebraic methods to find the values of the variables.
In educational settings, understanding how to solve these systems can be crucial for topics like vector spaces, transformations, or solving real-world problems modeled by linear relationships.
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