Example 2.  Consider the linear system  .  
2 (c).  Solve the linear system  AX = B  by using the Cholesky method.  

Solution 2 (c).

(i).  Enter the matrix and vector.  

(ii).  Construct the Cholesky factorization of matrix A.

(iii). Solve the linear system using our  ForeSub[n]  and  [BackSub[n]  subroutines.

First, solve the lower-triangular system    LY = B  for  Y.

Verify that  LY = B.

Second, solve the upper-triangular system    UX = Y  for  X.

Verify that  UX = Y.  

Therefore X is the solution to  LUX = B. and hence AX = B
And we can verify that it is the solution.

We can compare this solution with the solution obtained in parts (a) and (b).

(c) John H. Mathews 2004