Consider the n x n matrix Mn that contains all integers 1, 2,3........n2 as its entries

Chapter 2, Problem 44

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Consider the n x n matrix Mn that contains all integers 1, 2,3........n2 as its entries, written in sequence, column by column; for example,1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16A/4 =a. Determine the rank of M4. b. Determine the rank of Mn, for an arbitrary n > 2. c. For which integers n is Mn invertible?

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