Find the row interchanges that are required to solve the following linear systems using Algorithm 6.1.
a. x1 − 5x2 + x3 = 7,
10x1 + 20x3 = 6,
5x1 − x3 = 4
b. x1 + x2 − x3 = 1,
x1 + x2 + 4x3 = 2,
2x1 − x2 + 2x3 = 3
c. 2x1 − 3x2 + 2x3 = 5,
−4x1 + 2x2 − 6x3 = 14,
2x1 + 2x2 + 4x3 = 8.
d. x2 + x3 = 6,
x1 − 2x2 − x3 = 4,
x1 − x2 + x3 = 5.