ASAP,numerical Analyst use new raphson method and half interval method, Below is the transcription of the given image, which contains a system of linear equations:\[\begin{cases} x_1 + x_2 + x_3 = 6 \\2x_1 - x_2 + 4x_3 = 12 \\-3x_1 + 2x_2 - x_3 = -4 \end{cases}\]Explanation:The image shows a set of three linear equations involving three variables, $ x_1 $, $ x_2 $, and $ x_3 $. These equations can be solved using various methods such as substitution, elimination, or matrix operations to find the values of the variables. This system represents three planes in three-dimensional space, and their intersection points (if any) represent the solution to the system.

Answered: X1 + x2 + X3 = 6 2х, - х, + 4х3 —D 12…

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

ASAP,numerical Analyst use new raphson method and half interval method,

Below is the transcription of the given image, which contains a system of linear equations:

\[
\begin{cases}
x_1 + x_2 + x_3 = 6 \\
2x_1 - x_2 + 4x_3 = 12 \\
-3x_1 + 2x_2 - x_3 = -4
\end{cases}
\]

Explanation:

The image shows a set of three linear equations involving three variables, $ x_1 $, $ x_2 $, and $ x_3 $. These equations can be solved using various methods such as substitution, elimination, or matrix operations to find the values of the variables. This system represents three planes in three-dimensional space, and their intersection points (if any) represent the solution to the system.

Expert Solution

Step 1

As per Bartleby's answering policy, we can answer only one question, so kindly post the next question as another question and clearly state which question/ part is to be solved.

This question can be solved using the modified Newton Raphson method.

The formula for the modified Newton Raphson method is $[\begin{matrix} x_{1_{n + 1}} \\ x_{2_{n + 1}} \\ x_{3_{n + 1}} \end{matrix}]$ = $[\begin{matrix} x_{1_{n}} \\ x_{2_{n}} \\ x_{3_{n}} \end{matrix}] - A^{- 1} \times f ([\begin{matrix} x_{1_{n}} \\ x_{2_{n}} \\ x_{3_{n}} \end{matrix}])$