(a) Use LU factorization to solve the system of equations in Prob. 10.3. Show all the steps in the computation. 

(b) Also solve the system for an alternative right-hand-side vector

{b}^T = ⌊12 18 − 6⌋

Data From Problem 10.3

Use naive Gauss elimination to factor the following system according to the description in Section 10.2:

7x₁ + 2x₂ − 3x₃ = −12
2x₁ + 5x₂ − 3x₃ = −20
x₁ − x₂ − 6x₃ = −26

Then, multiply the resulting [L] and [U] matrices to determine that [A] is produced.