2. (Elementary Matrices, 12pt) You are given the matrix Convert A to reduced row echelon form using elementary row operations but implementing them as (left) matrix multiplications. E.g. the first operation would be E E21(2) which would correspond a) [6pt] Give the sequence of elementary operations, and the corresponding matrices E1, E2, E3, E4, E5, E6 so that E6E5E4E3E2E1A is in reduced row echelon form. You can use Matlab for all of this. Double-check that E6*E5*E4*E3*E2*E1*A is in reduced row echelon form. b) [5pt] We want to find an inverse of A; we know it exists, since rref(A)=I. We use three different ways to get the inverse: i) [2pt] Compute the inverse of A using E1, .., E6. Hint: remember that E6E5E4E3E2E1A=rref(A). ii) [2pt] Compute the inverse of A using the rref method we saw in class (working with rref(AI) ). iii) [1pt] Use the built-in inverse function supplied by Matlab to compute the inverse of A. c) [1pt] Compare AA(1) - I for the three different inverses computed in b). Do they differ significantly in quality? Is there a clear best/worst