Consider a sequence of real numbers r1, r2 .... rn such that no two numbers are equal. Using these numbers, we create ( N x N) square matrix R such that the ( i, j)-th element of R is given by

ai, j = rk, where k = min(i, j), i = 1,2,...., N; j = 1,2,....,N.

Write the elements of matrix R in terms of real numbers r1,r2,....,rn. Clearly show at least the top 4 x 4 and all the elements on the four corners.

And is this a symmetric matrix?