[change of basis] Consider the family β = (1 + x + x 2 , x − x 2 , 2 + x 2 ) of the polynomial space of degree ≤ 2, R2[x].

[change of basis] Consider the family ? = (1 + x + x 2 , x ? x 2 , 2 + x 2 ) of the polynomial space of degree ? 2, R2[x].

- Prove that ? of R2[x] is a basis of R2[x].
- Calculate M?can , the matrix for change of basis from the basis ? to the canonical basis of R2[x].
-Calculate the kernel and range of the matrix M?can
- If we were to change ? for any other basis of R2[x], would the kernel and range of M?can change?

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