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

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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

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

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 2022-4-18

编辑：Torsten 2022-4-18

y = L\(P*b)

is forward substitution,

x = U\y

is back substitution.

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

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