(a) Use nave Gauss elimination to decompose the following system according to the description in Sec. 10.2....

(a)

Use naïve Gauss elimination to decompose the following system according to the description in Sec. 10.2.

10x1 + 2x2 – x3 = 27

–3x1 – 6x2 + 2x3 = –21.5

x1 + x2 + 5x3 = – 21.5

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

(b) Use LU decomposition to solve the system. Show all the steps in the computation.

(c) Also solve the system for an alternative right-side vector: {B}T = [12 18 -6].