Example 1.  Create a 31 by 31 tridiagonal matrix A where the main diagonal elements are all "2" and all elements of the subdiagonal and superdiagonal elements are "1."  Then solve the linear system    where  .  Compute the solution using decimal arithmetic.  

Solution 1 (a).

The column form for B is:

The matrix A can be constructed with the command.

We can print out the system to be solved if we wish.

Solve the system Mathematica's built in  LinearSolve[A,B]  procedure.  

Notice that this linear system is producing some round off error near the 14th decimal place.

Verify the answer.

(c) John H. Mathews 2004