(a) Show experimentally that the n n matrix A = [ jk ] with jk...

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(a) Show experimentally that the n × n matrix A = [αjk] with αjk = j + k - 1 has rank 2 for any n. (Problem 20 shows n = 4.) Try to prove it.

(b) Do the same when αjk = j + k + c, where c is any positive integer.

(c) What is rank A if αjk = 2j+k-2? Try to find other large matrices of low rank independent of n.

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