Consider a sequence of positive real-numbers r1, r2, ., rN, such that no two numbers are the same.

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Consider a sequence of positive real-numbers r1, r2, ..., rN, such that no two numbers are the same.

Using these numbers, create two (N x N) square matrices A and B such that A is a lower triangular matrix and B is an upper triangular matrix.

The (i, j)-th element of A and B are given by :

a(i, j) = (i, j)-th element of A = ai,j = rj if i > j & ai,j = ri^2 if i = j. Also, ai,j = 0, otherwise. B = [A]T.

Write the elements of matrices A and B in terms of real-numbers r1, r2, ..., rN. Clearly, show at least the top 4 x 4 part and all the elements on the four corners.