1. The problem statement, all variables and given/known data Let B be a basis of R^2 consisting of the vectors <5,2> and <1,5> and let R be the basis consisting of <2,3> and <1,2> Find a matrix P such that [x]_r=P[x]_b for all x in R^2 2. Relevant equations Ax=B? 3. The attempt at a solution I attempted by using Ax=B as a format to solve for P, or x in the equation. I took the inverse of the column matrix of B because B is a basis, and if I am correct, a matrix's basis is defined as its coordinates ([x]_b). I understand the geometrical interpretation of a linear transformation, yet I have no idea how to represent the transformation as a matrix. I would love an in depth description to approach similar exercises.