Question

Compare between the (guassian,gauss-jordan and LU factorization)methods for solving linear systems from the following view points:
1) Storage requirements.
2) Computational requirements.
And hence suggest when to use each.

Answer 1

This is a subjective question, but I'll do my best. By storage requirements, you mean the amount of memory/mind power/etc. for your brain/calculator needs, right? The one that would need the most "storage" would be the LU factorization. You might have to do more computations for Gauss and Gauss-Jordan.

I personally hate LU factorizations you don't learn how to explicitly formulate them in elementary linear algebra, but you would use it when you have a lot of b's to calculate x for in the Ax = b equation. If you did Gauss or Gauss-Jordan, you would have to do elimination for b matrices, but you would only have to do ONE LU factorization.

Use Gauss and Gauss-Jordan when you only have to solve for x in Ax = b when you only have one or two b's. It's a lot faster.