Use Gaussian elimination with backward substitution and two-digit rounding arithmetic to solve the following linear systems. Do not reorder the equations. (The exact solution to each system is x1 = 1, x2 = −1, x3 = 3.)
a. 4x1 − x2 + x3 = 8,
2x1 + 5x2 + 2x3 = 3,
x1 + 2x2 + 4x3 = 11.
b. 4x1 + x2 + 2x3 = 9,
2x1 + 4x2 − x3 = −5,
x1 + x2 − 3x3 = −9.