4. Consider the matrix A = 6 7? -) = 2 -1 2 1 2. 1 2 1 (a) Compute AAT and obtain the singular values and a set of left singular vectors of A. (b) Find the "thin" SVD of A: A=ULV. U € R2x2 unitary, I; ER2x2, (c) Find the matrix B which is of rank 1 and which is the closest to the matrix A in the 2-norm sense. What is the 2-norm distance between A and B ? (d) Complete the columns of Vi of question (b) into an orthonormal basis of Rs and find the (full) SVD of A. (e) What is the null space of A? Find the vector of this null space that is the closest in the 2-norm sense to the vector 2 = {0 1 1 ] (f) What are all the least-squares solutions Ax = b where b = 18 8]? (g) Among the solutions found in (6) which one is the closest to the vector 2 = [2 1 -1 0 in the 2-norm sense?