# [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].

- Prove that β of R2[x] is a basis of R2[x].

- Calculate Mβcan , the matrix for change of basis from the basis β to the canonical basis of R2[x].

-Calculate the kernel and range of the matrix Mβcan

- If we were to change β for any other basis of R2[x], would the kernel and range of Mβcan change?

Alexa Rod

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## Answer

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Alessandro Iraci

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The answer is accepted.

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