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Generate a matrix A by setting A-round(10 rand(6)) and generate a vector b by setting b=round(20*(rand(61)-05)) 1. Since A was generated randomly, we would expect it to be nonsingular. The sys- tem Ar-b should have a unique solution (1) Find the solution using the operation. (2) Use MATLAB to compute the reduced row echelon form U of A (3) How does the last column of U compare with the solution r? (4) In exact arithmetic they should be the same. Why? Explain (5) Compute the difference U(:, 7) x using format long. 2. Let us now change A so as to make it singular. Set A(:, 3) A(:, 1 : 2) * [43], (1) Use MATLAB to compute rref ([A b]) (2) How many solutions will the systern Ax = b have? Explain. 3. Set y-round (20*(rand(6,1)-0.5)) and c A y (1) Why do we know that the system Ax must be consistent? Explain (2) Compute the reduced row echelon form U of [Ac (3) How many solutions does the system Al-C have