2. (Solving linear systems)

Consider the linear system Ax = b

with A =[14 9 14 6 -10;-11 -11 5 8 6;15 -2 -14 8 -15;14 13 11 -3-7;0 9 13 5 -14], and . b = [-4;8;6;0;10].

a) Verify that the linear system has a unique solution.Hint: use rref, rank, det, or any other Matlab method.Briefly explain the answer please.

You'll now solve Ax = b in three different ways. Store the threedifferent solutions in four different variables (x1,x2,x3,x4, say),we need to compare them in parts c and d.

b1) Using rref, determine the solution x of the system Ax = b,and store it in variable x1. Hint: x1 is the final columnof the reduced row echelon form of M = (A|b). Remember horzcat.

b2) Using Matlab's linsolve method, find a solution to thesystem Ax = b. Store the solution in x2.

b3) Using Matlab's inverse method (^(-1) or inv), solve thesystem as x = A^(-1)b, store the result in x3.

b4) Use the rref method from class to find an inverse matrix Bof A. Use that to calculate x = Bb. Store the result in x4.

c) Compare the solutions x1, x2, x3,x4. Do any two of themagree? Does that contradict a) or not?

d) Try ranking the solutions by quality. To do so, compute Ax-b,for the various values of x, and see which x produces the smallestdifference between Ax and b.