Today in Mathland we ventured on down to down town Augmentia, and learned about solving systems using matrices. There are different ways to do so, but my favorite is using Gauss Jordan Elimination. It's just like Gaussian elimination, but you take it a step further.
In Gaussian elimination as shown above, you must follow the 3 steps.
1. Write the Augmented Matrix
2. Use ERO's to rewrite in row echelon form
3. Write system of equations and use back substitution
The difference in Gaussian Jordan Elimination, is that you solve to get all 1's on your main diagonal, but also you must make all other spaces in the Augmented Matrix equal 0. Then you won't need to back substitute because your answer will be right there in front of you. Here are some examples.
Augmented Matrices can seem elaborate at times, but following the steps of Gaussian or Gaussian Jordan Elimination will give you clear and concise guidelines to make it as easy as possible.
I have to agree with you I like Gaussian Jordan elimination because we don't need to go back and do back substitution. However Gaussian elimination can be faster and easier for some people. Thank you for doing a problem to show us both the Gaussian Jordan elimination and Gaussian elimination. You also explained the differences very well.
ReplyDeletethanks for clearly distinguishing between the Gaussian and Gauss Jordan method of elimination. Though i dislike both ways, I have to agree with both Marissa and you that I prefer the Gauss Jordan method! It is much simpler and easier to follow with your mind because you don't have to switch between doing some matrix manipulation then some equation manipulation. Thanks for the examples too, they are very clear and straightforward.
ReplyDeletethank you for discussing this. I found that looking at the steps written out while actually doing them made for an easy time solving the problem! the steps written out and then you elaborating on them made it very concise.
ReplyDelete