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I'm having some trouble understanding basis and how they relate to transformation matrices.
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] (Matlabnotation).
Find F:s matrix representation in the basis f_1= e_12e_2+e_4 , f_2=3e_2e_3e_4, f_3=e_3+e_4, f_4=2e_4.

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?
Homework Statement
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] (Matlabnotation).
Find F:s matrix representation in the basis f_1= e_12e_2+e_4 , f_2=3e_2e_3e_4, f_3=e_3+e_4, f_4=2e_4.
Homework Equations

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?