Problem 3: LU decomposition

Given the following system of equations:

7x1+2x2-3x3 = -12,

2x1 + 5x2-3x3 = -20,

x1-x₂-6x3 = -26.

(A) Use naive Gauss elimination to decompose the system (follow Chapra §10.1.2). Mul-

tiply the resulting [L] and [U] matrices to confirm that [A] is produced.

(B) Use LU decomposition to solve the systme. Show all the steps in the computation.

(C) Solve the system for an alternative right-hand side vector: b = [12, 18,-6].