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

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Jonas Morgner
Jonas Morgner 2022-4-17
编辑： Torsten 2022-4-18
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

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Sam Chak
Sam Chak 2022-4-17
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
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Jonas Morgner
Jonas Morgner 2022-4-18
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
Torsten 2022-4-18
编辑：Torsten 2022-4-18
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.

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