Provide the details of the proof that a one-pass matrix multiplication algorithm requires replication rate at least r 2n^2/q, including: (a) The proof that, for a fixed reducer size, the maximum number of outputs are covered by a reducer when that reducer receives an equal number of rows of M and columns of N. (b) The algebraic manipulation needed, starting with (sigma from k to i=1) q^2 4n^4