Question: For each of the following linear systems find a permuted L U factorization of the coefficient matrix and then use it to solve the system

For each of the following linear systems find a permuted L U factorization of the coefficient matrix and then use it to solve the system by Forward and Back Substitution.
(a) 4x1 - 4x2 + 2x3 = 1
-3x1 + 3x2 + x3 = 3
-3x1 + x2 - 2x3 = -5
(b) y - z + w = 0
y + z= 1
x - y + z - 3w = 2
x+2y - z + w= A
(c) x - y + 2z + w = 0
-x + y - 3z= 1
x - y + 4z - 3w = 2
x + 2y - z + w= 4

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