Set A = triu(ones(5)) * trill one s(S). If L dcnoc, the linear operator defined L(x) = Ax for all x in Rn. then A is the matrix representing L. with respect to the standard basis for R5. Construct a 5s x 5 Inatro. U by setting
U = hankel(ones(5. 1) 1: 5).
Use the MATLAB function rank to verify that the column vectors of U are linearly independent. Thus E = [u1 u2, u3, u4 u5] is an ordered basis for R. The matrix U is the transition matrix from E to the standard basis,
(a) Use MATLAII to compute the matrix B representing L with respect to E. The matrix × B should he computed in terms of A. U, and U-1.)
(b) Generate another matrix by setting
V = toeplitzl(1,01,1,1,)
Use MAII.AH 10 che ihai V is nonsingubr. It follow that the colum sectors of V arelinearly independent and hence form an ordered basis F (or R. UseMATLAB to compute the matrix C. which represent L with respect to F. (The matrix C should he computed in term of A. V. and V-1
(c)The matrices B and C from parts (a and (N should be similar. Why? Explain. Use MATLAB to compute the transition matrix S from F to E. compute matrix C in terms of 8, S. and S'. Compare sour result with the result from pan (b).