Solving Transformation Matrix and Basis Problem

[Gramsci]

I'm having some trouble understanding basis and how they relate to transformation matrices.

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] (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.

Homework Equations

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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?

 

[Gunthi]

The e's represent the usual euclidian base e1 = (1,0,0,0), e2=(0,1,0,0) etc...

 

[vela]

I'm having some trouble understanding basis and how they relate to transformation matrices.

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] (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.

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?

That's what you want to do, but I think you're trying to invert the wrong matrix.