numerical matrix analysis

Let A E Rmxn have a reduced SVD A = oiuivT =1 where the ui E Rm and the vi E R" are the left and right singular vectors. Let x E Rn. (a) How many operations are required to compute Ax using the full m x n matrix A? (b) How many operations are required to compute oiuiv, x? Hint: Organise your computations efficiently. (c) How many operations are required to compute Axx where Ak = _-jojuju? ? Briefly, when might it be advantageous to compute Ax using the reduced SVD form of A or a lower rank approximation Ak