Modify the LU Factorization Algorithm so that it can be used to solve a linear system, and then solve the following linear systems.
a. 2x1− x2+ x3 = −1,
3x1+3x2+9x3 = 0,
3x1+3x2+5x3 = 4.
b. 1.012x1 − 2.132x2 + 3.104x3 = 1.984,
−2.132x1 + 4.096x2 − 7.013x3 = −5.049,
3.104x1 − 7.013x2 + 0.014x3 = −3.895.
c. 2x1 = 3,
x1 + 1.5x2 = 4.5,
− 3x2 + 0.5x3 = −6.6,
2x1 − 2x2 + x3 + x4 = 0.8
d. 2.1756x1 + 4.0231x2 − 2.1732x3 + 5.1967x4 = 17.102,
−4.0231x1 + 6.0000x2 + 1.1973x4 = −6.1593,
−1.0000x1 − 5.2107x2 + 1.1111x3 = 3.0004,
6.0235x1 + 7.0000x2 − 4.1561x4 = 0.0000