Consider three systems of equations defined by: H x = b , n = size of H. We will take n = 11,12 and 13, where b is a vector chosen in such a way that the exact solution of our system is [1 1 1 1 …. 1].

(a) Write a program or use the one from our book’s website( https://sites.google.com/site/numericalanalysis1burden/home ), that performs Gaussian Elimination (without pivoting) to compute the solution for each n (3 solution vectors in all). Your program should also keep track of the number of multiplications (divisions). The OUTPUT should consist of the solution vector x, and the norm of the error vector, as shown in the example below:

for n = 5, the exact solution is = Transpose of [1.0 1.0 1.0 ……… …… ]

computed solution = Transpose of [0.9937 0.999 1.0001 …..]

error = exact solution minus computed solution = Transpose of [0.0063 0.001 0.0001 ….. ]

infinity norm of the error vector is = 0.0063

Euclidean norm of the error vector is = 0.0235

Number of multiplications in my computer program = yyyy

Number of multiplications for n=5, using the formula in our book, my answer should have been: __________

As shown above, write the seven bullet items for each case, n=11, case n=12 and case n=13. Put the answers here and proceed to part (b)

(b) Comment on the sources of error for parts (a). Type your answer here:

(c) Over here, copy the Gaussian Elimination computer program that you used in part (a).