Solve Linear System with Gaussian Elimination

In summary, the conversation is about solving a linear system using Gaussian elimination and 3-digit rounding arithmetic. The person is having trouble understanding the textbook and is looking for help. They are also directed to a website that can provide step-by-step instructions on solving the problem.
  • #1
Newbatmath
12
0

Homework Statement



Hey everyone! I was handed this question in class without being taught how to do it! The text is supposed to be helpful but it is just confusing.

Using Gaussian elimination and 3-digit rounding arithmetic, solve the following linear system:

3.3330x_1 +15920x_2 +10.333x_3 = 7953
2.2220x_1 +16.710x_2 +9.6120x_3 = 0.965
-1.5611x_1 +5.1792x_2 -1.6855x_3 = 2.714

I'm then supposed to compare it to the actual solutions of x_1 = 1, x_2 = 0.5 and x_3 = -1 but I believe I know how to do that. :)

If there is anyway you can let me know how to do the above problem I'd really appreciate it! I want to learn this and the textbook is not clear at all.
 
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  • #3
Note that the above link takes it a step further with Gauss-Jordan elimination.

Just simply quit when you have reached the requirements for regular Gaussian elimination.
 

What is Gaussian Elimination and how does it work?

Gaussian Elimination is a method of solving a system of linear equations by using elementary row operations to transform the system into an equivalent system in echelon or reduced echelon form. This process involves using addition, subtraction, and multiplication to eliminate variables and solve for the remaining variables.

Why is Gaussian Elimination an effective method for solving linear systems?

Gaussian Elimination is an effective method because it allows for the systematic elimination of variables, making it easier to solve for the remaining variables. It also reduces the chances of making errors compared to other methods such as substitution or graphing.

What are the main steps involved in solving a linear system using Gaussian Elimination?

The main steps involved in Gaussian Elimination are: 1) writing the system of equations in matrix form, 2) using elementary row operations to transform the matrix into echelon or reduced echelon form, 3) rewriting the matrix into a system of equations, and 4) solving for the variables using back substitution.

What are the advantages and disadvantages of using Gaussian Elimination to solve linear systems?

Advantages of Gaussian Elimination include its systematic approach, reduced chances of errors, and ability to solve large systems of equations. Some disadvantages include the potential for round-off errors and the need for a large amount of computation for complex systems.

How does Gaussian Elimination compare to other methods of solving linear systems?

Gaussian Elimination is generally considered to be more efficient and accurate than other methods such as substitution or graphing. It is also more versatile and can be used to solve a wider range of systems, including those with more than two variables.

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