Ise the Gauss-Seidel Method to solve the system below. Use initial approximation (0,0). Give your answers to the first 3 approximations to 4 decimal places. 2x1 + X2 = 1 K1 + 4x2 = -3 le sure to use 4 decimal places. nitial approximation: X1= 0, x2 = 0 irst iteration: x1= Fecond iteration: X1= hird iteration: x- , x2 X2
Ise the Gauss-Seidel Method to solve the system below. Use initial approximation (0,0). Give your answers to the first 3 approximations to 4 decimal places. 2x1 + X2 = 1 K1 + 4x2 = -3 le sure to use 4 decimal places. nitial approximation: X1= 0, x2 = 0 irst iteration: x1= Fecond iteration: X1= hird iteration: x- , x2 X2
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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![### Applying the Gauss-Seidel Method to Solve a System of Linear Equations
In this exercise, we will solve the given system of linear equations using the Gauss-Seidel method.
#### System of Equations:
\[
\begin{aligned}
2x_1 + x_2 &= 1 \\
x_1 + 4x_2 &= -3
\end{aligned}
\]
#### Initial Approximation:
\[
\begin{aligned}
x_1 &= 0 \\
x_2 &= 0
\end{aligned}
\]
Be sure to use 4 decimal places.
#### Iterative Process:
##### First Iteration:
\[
\begin{aligned}
x_1 &= \boxed{} \\
x_2 &= \boxed{}
\end{aligned}
\]
##### Second Iteration:
\[
\begin{aligned}
x_1 &= \boxed{} \\
x_2 &= \boxed{}
\end{aligned}
\]
##### Third Iteration:
\[
\begin{aligned}
x_1 &= \boxed{} \\
x_2 &= \boxed{}
\end{aligned}
\]
In each iteration, you are required to update \( x_1 \) and \( x_2 \) based on the new values obtained from the previous iteration. Please provide your answers to the first three approximations up to 4 decimal places in the provided boxes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42f67b29-db3a-470e-8f57-9956af53c593%2F4f9dbe80-5655-4ea1-b890-ff105cf897fb%2Fjns8hwh_processed.png&w=3840&q=75)
Transcribed Image Text:### Applying the Gauss-Seidel Method to Solve a System of Linear Equations
In this exercise, we will solve the given system of linear equations using the Gauss-Seidel method.
#### System of Equations:
\[
\begin{aligned}
2x_1 + x_2 &= 1 \\
x_1 + 4x_2 &= -3
\end{aligned}
\]
#### Initial Approximation:
\[
\begin{aligned}
x_1 &= 0 \\
x_2 &= 0
\end{aligned}
\]
Be sure to use 4 decimal places.
#### Iterative Process:
##### First Iteration:
\[
\begin{aligned}
x_1 &= \boxed{} \\
x_2 &= \boxed{}
\end{aligned}
\]
##### Second Iteration:
\[
\begin{aligned}
x_1 &= \boxed{} \\
x_2 &= \boxed{}
\end{aligned}
\]
##### Third Iteration:
\[
\begin{aligned}
x_1 &= \boxed{} \\
x_2 &= \boxed{}
\end{aligned}
\]
In each iteration, you are required to update \( x_1 \) and \( x_2 \) based on the new values obtained from the previous iteration. Please provide your answers to the first three approximations up to 4 decimal places in the provided boxes.
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