Use the Gaussian Elimination Algorithm to solve the following linear systems, if possible, and determine whether row interchanges are necessary:
a. x1 − x2 + 3x3 = 2,
3x1 − 3x2 + x3 = −1,
x1 + x2 = 3.
b. 2x1 − 1.5x2 + 3x3 = 1,
−x1 + 2x3 = 3,
4x1 − 4.5x2 + 5x3 = 1
c. 2x1 = 3,
x1 + 1.5x2 = 4.5,
− 3x2 + 0.5x3 = −6.6,
2x1 − 2x2 + x3 + x4 = 0.8
d. x1 + x2 + x4 = 2,
2x1 + x2 − x3 + x4 = 1,
4x1 − x2 − 2x3 + 2x4 = 0,
3x1 − x2 − x3 + 2x4 = −3.