Help with 7x7 gauss jordan elimination program

[dudeweresdeth]

Homework Statement

Hi, I am new to gauss jordan elimination and our teacher onlt taught us how to solve a 3x3 equation and gave us a 7x7 problem to answer due tom.

2m + 3n - p + q + 2r - s + 2t = 1
m - n + p - q + r + s + t = 2
2m + 2n - 2p + q - 2r + s - t = 1
m - 2p + q - r - s + t = 1
m - 2n + p - q + r + s + t = 2
m + 2n + 2p + 2q + r - s + 2t = 1
m - n - 2p - q - r + s + t = 2

Homework Equations

2m + 3n - p + q + 2r - s + 2t = 1
m - n + p - q + r + s + t = 2
2m + 2n - 2p + q - 2r + s - t = 1
m - 2p + q - r - s + t = 1
m - 2n + p - q + r + s + t = 2
m + 2n + 2p + 2q + r - s + 2t = 1
m - n - 2p - q - r + s + t = 2

The Attempt at a Solution

i tried solving it thrice . . . using different methods i saw on the internet, but I am scared i don't want to fail. I really need help pls help me out dudes.

tahnks!

 

[Defennder]

First thing you should do is to write out the equations in the form of a matrix:

The entries of the matrix should consist only of the co-efficients of the unknowns. Then just juxtapose the numbers on the RHS of the system of equations to form an augmented matrix. Then perform row-reduction. Where are you stuck? It's hard to help if you don't show any work.

 

[Architeuthis Dux]

Hi there,

I understand that you are struggling with a 7x7 gauss jordan elimination problem and are looking for help. I can provide some guidance and tips that may help you solve this problem.

Firstly, it's important to understand the steps involved in gauss jordan elimination. This method is used to solve a system of linear equations by transforming the equations into a simpler form. The goal is to reduce the system to an equivalent system where the coefficients of the variables are in a diagonal line.

To solve a 7x7 problem, you will need to follow the same steps as you would for a 3x3 problem, but with more variables and equations. It may seem daunting at first, but with practice and patience, you can definitely solve this problem.

Here are some tips that may help you:

1. Start by organizing the equations in a matrix form. This will make it easier to keep track of the variables and coefficients.

2. Use row operations such as adding, subtracting, or multiplying rows to eliminate variables. Remember, whatever operation you perform on one row, you must do the same on the other rows to keep the system equivalent.

3. Keep track of the row operations you perform. This will help you avoid mistakes and also make it easier to backtrack if needed.

4. Once you have reduced the system to a diagonal form, use back substitution to solve for the variables.

Remember, practice makes perfect. If you are still struggling, I suggest seeking help from your teacher or a tutor. Don't be afraid to ask for help, it's important to understand the concepts rather than just getting the right answer.

I hope this helps and good luck with your problem!