I have the following question: Is there a basis for the vector space of polynomials of degree 2 or less consisting of three polynomial vectors ##\{ p_1, p_2, p_3 \}##, where none is a polynomial of degree 1?(adsbygoogle = window.adsbygoogle || []).push({});

We know that the standard basis for the vector space is ##\{1, t, t^2\}##. However, this wouldn't be allowed because there is a polynomial of degree 1 in this basis.

I'm thinking that there is not a basis without a polynomial of degree 1, but can't seem to formalize it.

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# I Existence of basis for P_2 with no polynomial of degree 1

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