I'm having some trouble understanding basis and how they relate to transformation matrices. 1. The problem statement, all variables and given/known data Let e_1,e_2,e_3,e_4 be a basis in a four dimensional vector space V. Suppose that the linear transformation F on V has the matrix representation: [1 0 2 1;-1 2 1 3;1 2 5 5;2 -2 1 -2] (Matlab-notation). Find F:s matrix representation in the basis f_1= e_1-2e_2+e_4 , f_2=3e_2-e_3-e_4, f_3=e_3+e_4, f_4=2e_4. 2. Relevant equations - 3. The attempt at a solution I thought of using B^(-1)AB (B is the basis A the transformation matrix), but I can't invert our basis here. What should I do?