Let A be a matrix whose singular value decomposition is given by Make use of the singular

Question:

Let A be a matrix whose singular value decomposition is given by

Make use of the singular value decomposition to do each of the following.
(a) Determine the rank of A.
(b) Find an orthonormal basis for R(A).
(c) Find an orthonormal basis for N(A).
(d) Find the rank 1 matrix B that is the closest matrix of rank 1 to A (distance between matrices is measured using the Frobenius norm).
(e) Let B be the matrix asked for in part (d). Use the singular values of A to determine the distance between A and B (i.e., use the singular values of A to determine the value of ||B - A||F).