Let z be the n × 1 column vector all of whose entries are equal to 1.
(a) Show that if A is an m × n matrix, the ith entry of the product v = Az is the ith row sum of A, meaning the sum of all the entries in its ith row.
(b) Let W denote the n × n matrix whose diagonal entries are equal to 1-n/n and whose offdiagonal entries are all equal to 1/n. prove that the row sums of B = AW are all zero.
(c) Check both results when

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