In case we are asked to solve for a monomial interpolant, can we use RREF form and solve?

[kuriant1]

Instead of LU factorization etc

Thanks!

[ccc]

You can use any method to solve the arising linear system.
However, I am not sure how different RREF would be from
using LU factorization, except you just take care of the right-hand-side
simultaneously and do not keep track of the L entries.