### Applying the Gauss-Seidel Method to Solve a System of Linear EquationsIn 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.

There are numerous numerical methods to solve a system of linear equations. By solving the same…

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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Question

### 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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