- #1
Mr Davis 97
- 1,462
- 44
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?
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.
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.