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. −x1 + 4x2 + x3 = 8,
5/3 x1 + 2/3 x2 + 2/3 x3 = 1,
2x1 + x2 + 4x3 = 11
b. 4x1 + 2x2 − x3 = −5,
1/9 x1 + 1/9 x2 - 1/3 x3 = −1,
x1 + 4x2 + 2x3 = 9.