Numpy and Python. Create a 1000x1000 matrix A with random numbers and a random number vector b with 1000 elements. Solve the simultaneous equation Ax = b in the following ways:

i) By using the inverse of A, i.e. A^-1, with numpy.linalg.inv and then solving for Ax = b.

ii) By using numpy.linalg.solve

Find the estimation error in the solution, ||Ax - b||. It should be very close to zero.

Use @timeit to find how long it takes to use i and ii.

What difference is the between the results? Why is there a difference?

Start with the following code:

A = np.random.rand(1000,1000)

b = np. random.rand(1000)

*enter rest of code here*