Use the Gaussian Elimination Algorithm to solve the following linear systems, if possible, and determine whether row interchanges are necessary:
a. x2 − 2x3 = 4,
x1−x2 + x3 = 6,
x1 − x3 = 2.
b. x1 − 1
2 x2 + x3 = 4,
2x1 − x2 − x3 + x4 = 5,
x1 + x2 + 1
2 x3 = 2,
x1 − 1
2 x2 + x3 + x4 = 5
c. 2x1−x2+x3−x4 = 6,
x2−x3+x4 = 5,
x4 = 5,
x3−x4 = 3.
d. x1 + x2 + x4 = 2,
2x1 + x2 − x3 + x4 = 1,
−x1 + 2x2 + 3x3 − x4 = 4,
3x1 − x2 − x3 + 2x4 = −3.