someone help me please. thank you

Question

Consider a system of linear equations as follow:

8x1 + 6x2 + 33x3 = 3,

4x1 + 4x2 + 8x3 = 7,

4x1 + 8x2 + 6x3 = −12.

(a) If the given system above can be re-written in the matrix equation form of Ax = b, show that the matrix A is a symmetric positive definite matrix.

(b) Then, solve the system by using Cholesky method.

Answer 1

(x1, x2, x3) = (621/64, -345/64, -41/32)

= about (9.7, -5.4, -1.3)