How to do an elimination procedure to represent the solution (matrix)

Apply the elimination procedure until you reach a matrix that represents

the solution (identity matrix + column with the values for x1, x2 and x3,

see slide 1.1-14 from Linear Algebra). Include each step (code needed)

in the report and explain the process.

The polynomials:

x1 - 2x2 + x3 = 0

2x2 - 8x3 = 8

-4x1 + 5x2 +9x3 = -9

Answer 1

[Sam Chak]

Can you show the slides and elimination formulas? Otherwise, I think this elimination procedure:

A = [1 -2 1;
       0 2 -8;
      -4 5 9]

b = [0; 8; -9]

[L, U, P] = lu(A)

y = L\(P*b)

x = U\y

[Jonas Morgner]

Hey Sam, that totally worked thank you!

[Jonas Morgner]

I just got one question. If I am undestanding your code correctly, the y = L/(P*b) and x = U/y are the factors to solve the linear system right?

[Torsten]

y = L\(P*b)

is forward substitution,

x = U\y

is back substitution.

https://courses.engr.illinois.edu/cs357/sp2020/notes/ref-9-linsys.html

Be careful with the direction of the slash - above, you did it wrong.