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Modify the LU Factorization Algorithm so that it can be used to solve a linear system, and then solve the following linear systems.

a. x1 − x2 = 2,

2x1 + 2x2 + 3x3 = −1,

−x1 + 3x2 + 2x3 = 4

b. 1/3 x1 + 1/2 x2 - 1/4 x3 = 1,

1/5 x1 + 2/3 x2 + 3/8 x3 = 2,

2/5 x1 - 2/3 x2 + 5/8 x3 = −3.

b. 2x1 + x2 = 0,

−x1 + 3x2 + 3x3 = 5,

2x1 − 2x2 + x3 + 4x4 = −2,

−2x1 + 2x2 + 2x3 + 5x4 = 6

d. 2.121x1 − 3.460x2 + 5.217x4 = 1.909,

5.193x2 − 2.197x3 + 4.206x4 = 0,

5.132x1 + 1.414x2 + 3.141x3 = −2.101,

−3.111x1 − 1.732x2 + 2.718x3 + 5.212x4 = 6.824

a. x1 − x2 = 2,

2x1 + 2x2 + 3x3 = −1,

−x1 + 3x2 + 2x3 = 4

b. 1/3 x1 + 1/2 x2 - 1/4 x3 = 1,

1/5 x1 + 2/3 x2 + 3/8 x3 = 2,

2/5 x1 - 2/3 x2 + 5/8 x3 = −3.

b. 2x1 + x2 = 0,

−x1 + 3x2 + 3x3 = 5,

2x1 − 2x2 + x3 + 4x4 = −2,

−2x1 + 2x2 + 2x3 + 5x4 = 6

d. 2.121x1 − 3.460x2 + 5.217x4 = 1.909,

5.193x2 − 2.197x3 + 4.206x4 = 0,

5.132x1 + 1.414x2 + 3.141x3 = −2.101,

−3.111x1 − 1.732x2 + 2.718x3 + 5.212x4 = 6.824

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