Let A be an n x n matrix and b a column vector with n entries. Consider solving the

linear system Az = b. If only one vector b is given, then the fastest method for solving

the system in Matlab is x=A\b. Note that is a Matlab operator.

However the situation is different if we need to solve many linear systems Az = b

with the same matrix A and different right-hand side vectors b. You will compare the

efficiency of the following two methods in case of solving many systems Az = b with the

same matrix A:

• z =A\b. You can refer to this method as the "built-in solver."

• Compute the LU decomposition of A = LU. Solve y = L\b and then z = U\y. The

Matlab command to compute L and U is lu. Of course, the LU decomposition of A

needs to be computed only once.

You are going to look at the efficiency (in terms of computation time) of these two

methods, using random linear systems of large size.

Below are the precise instructions of what needs to be done: