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**[SOLVED] Linear algebra; changing bases**

## Homework Statement

I have two bases E and F given by:

E = [1, x, x^2]

F = [1-x, x-x^2, x^2].

I want to find the transition-matrix S that goes from E to F.

## The Attempt at a Solution

To do this, I must write one basis as a linear combination of the other. I am just confused about which way?

Since we are going from E to F, I believe I have to write F as l.c. of E, so for 1 - x we have the vector (1,-1,0)^T. Am I right or is it the other way around?

I hope you can help, thanks in advance.