Topic Linear Algebra Can someone please explain the differen

Topic: Linear Algebra

Can someone please explain the difference between Gaussian Elimination and LU Decomposition? While looking at both, I noticed that the methods are relatively similar and do not see a difference. Which method is better and how do I know which one to use? Thanks!!

Solution

for 3x3 matrix(x,y,z)
in Gaussian you get

a row1col1=1
a row1 col2 =0
a row1 col3=0
--------------------
a row2 col2 =1
a row 3 col2=0
a row3 col3=1
it would look like this
|1....a12....a13....A|
|.0....1.......a23....B|
|0.....0.......1........C|
whereas
in Naive G.E
it would be
| a11...a12...a13...A|
|.0.......a22...a23...B|
|0........0.......a33..C|
the you do back substitution to find x,y,z