What's the difference between these 2 problems?

[Math10]

Problem 1: Use Gaussian elimination with back substitution to solve the following system.
Problem 2: Use the Gauss-Jordan method to solve the following system.

I've worked on both of these types of problems but I didn't notice the difference between these 2 types of problems. Aren't the Gaussian elimination with back substitution and the Gauss-Jordan method the same thing?

 

[SteamKing]

It doesn't really matter as long as you solve the system. The history of the method is long and twisting and the naming is also confusing:

http://en.wikipedia.org/wiki/Gaussian_elimination

 

[verty]

The wikipedia page is not at all clear, search for "Gauss-Jordan" to see where it talks about it.

 

[SteamKing]

The wikipedia page is not at all clear, search for "Gauss-Jordan" to see where it talks about it.

Exactly. That's why I said what I said.

 

[AlephZero]

The important thing is the general idea of performing elementary row operations on a matrix to make some of the matrix elements zero. There are more than two practical ways to do this.

IMO debating exactly who discovered (or rediscovered) which particular method is a question for historians, not mathematicians.

 

[Math10]

Thanks for the help, guys.

 

[micromass]

Gaussian elimination is not at all the same as Gauss-Jordan elimination. Gaussian elimination is always the more efficient way to solve equation. Gauss-Jordan is only really useful for theoretical purposes.

More information (with a nice analysis of the difference between Gauss and Gauss-Jordan) can be found in Meyer: https://www.amazon.com/dp/0898714540/?tag=pfamazon01-20