Please run 20 tests in Matlab as the problem is required.

6. Consider the following two ways of solving a 2-by-2 linear system of equations: Ar = = = b 21 a 22 Algorithm 1. Gaussian elimination with partial pivoting. (You can use the Matlab command \\) Algorithm 2. Cramer's rule (see textbook Page 67-68): det(A) = 011 * 022 - 012 * 021, T1 = (022 * b1 - 012 * b2)/ det(A), 12 = (-a21 * b1 + all * b2) / det(A). Show by means of numerical examples that Cramer's rule is not backward stable. Please include your code and results in the answer. Hint: Choose a matrix which is nearly singular: A(:,2) ~ A(:, 1) and b ~ A(:, 2). You can construct A(:, 2) by adding a random perturbation (Matlab command rand) of small norm to A(:, 1) and construct b from A(:, 2) similarly. Run 20 tests and demonstrate your results. You can estimate the relative backward error using the formula 116 All = where a is the computed solution and r = A - br is the residue