Suppose A is 10 by 10 and A2 = 0 (zero matrix). This means that the column space of A is
Chapter 3, Problem 46(choose chapter or problem)
Suppose A is 10 by 10 and A2 = 0 (zero matrix). This means that the column space of A is contained in the, . If A has rank r, those subspaces have dimension r < 10 - r. So the rank IS r < 5. (This problem was added to the second printing: If A2 = 0 it says that r < n/2.)
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