Lost with the below matrix problem. Care to share how to solve it?

Thank you so much.

Q: Consider a sequence of real-numbers

*r*1, *r*2, …, *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?