Problem 2. Let (X, R) be a linear space and let the following three finite sets be basis sets for X: S. = {x1, 2, ... ,In}, S. = {T1,72,.…..,In}, and Ŝ, = {î1,î2, ... ,ân}. If the representation of...

Extracted text: Problem 2. Let (X, R) be a linear space and let the following three finite sets be basis sets for X: S. = {x1, 2, ... ,In}, S. = {T1,72,.…..,In}, and Ŝ, = {î1,î2, ... ,ân}. If the representation of each vector in 5, with respect to S, is given by the columns of the matrix P, and if the representation of each vector in Ŝ, with respect to 5, is given by the columns of the matrix Q, explain how to determine the representation of each vector in S, with respect to Ŝ..