Lost with the below matrix problem. Care to share how to solve it?
Thank you so much.


Q: Consider a sequence of real-numbers
r1, r2, …, rN. Using these we create
an (N × N) square matrix R such that the (i, j)-th element of R is given by rk, where k = max(i, j), i = 1, 2, …, N; j = 1, 2, …, N.
A.


Write the matrix R in terms of its elements. Clearly, show at least the top 3 × 3 part and all the elements on the four corners.
B.


Is this a symmetric matrix?
C.


Define a (N × N) matrix called contra-identity as J . Compute the matrix-matrix product S = R J.
D.


Carry out appropriate EROs to reduce the matrix S to its echlon form.
E.


Carry out appropriate EROs to reduce the matrix S to its row echlon form.
F.


Carry out appropriate EROs to reduce the matrix S to its reduced row echlon form.
G.


It is said that a unique solution always exists for solving the linear system Sx = b. Is that true?