(12 points) A Hilbert matrix is an n x n symmetric matrix in which each entry ay 1/i+j-1). Use the command hilb ( n ) in Matlab to create a set of Hilbert matrices H, for n = 1 to 8, and use the command inv (H) in Matlab to compute the inverse of each of these matrices. At what value of n does HH 1? Use the command cond() in Matlab to compute the condition numbers of H and H. Please provide a printout of your results and any code you wrote to obtain them. 5. 6. (16 points) Consider the 2 x 2 matrivns-1 2 and the vector = 1-2 2-2-i 3-2-i+1 Use the Matlab function rref () to compute the reduced echelon form of A for increasingly large values of i. At what value of i does the reduced echelon form cease to show a pivot in every row? a. b. Use the Matlab function rank( to compute the rank of A. At what value of i does A cease to have full rank? Is this the same value of i at which the reduced echelon form of A ceases to be equal to the identity? Use the Matlab function inv() to compute the inverse of A. At what value of i is Matlab c. unable to compute A-1? Is this the same value of i at which A ceases to have full rank? v for increasingly large values of. [You can 2 d. Use Matlab to solve the linear system Ax use the expression x Alv.] At what value of i does the solution x cease to equal (1, 1)? A what value of i is Matlab unable to return a solution for x? What do you conclude about the method Matlab uses to compute x = Alv? 1