There are actually two reasons I am posting this question(Which has 3 parts)
1) Because it's really fun
2) Because I can't figure out parts 2 and 3.
Apply elimination to produce the factors L and U for
Part 1: A =
Part 2: A =
Part 3: A =
Now for the first one, what I did was(and I hope I get the notation on this right)
E = Elimination Matrix,
EA = This produced
Multiply by A, to get
U =
A=LU since this brought me back to A, I knew I was right...
Now when getting into the 3x3 matrices, I started getting into trouble.
Do I basically use a guess and check method? Or is there a way I can systematically solve this using elimination matrices and LU?
Are Row Exchanges necessary for part 2 and 3?
Can I avoid using Guess and Check for L and U?
Also I'm going to put what I did in Part 1 in Matrix Notation(or at least attempt to) and was wondering if someone could tell me if it is correct.
Which would produce