(a) Show experimentally that the n n matrix A = [ jk ] with jk = j + k - 1 has rank

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

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

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