Let V be the vector space of the polynomials of degree 2 over . Prove that the polynomials: span, or are a generating system of, V. If I solve the system of linear equations- how do I prove that they span V? Thanks.
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Originally Posted by bmp05 Let V be the vector space of the polynomials of degree 2 over . Prove that the polynomials: . You just need to show these polynomial are linearly independent. Say that where is the zero-polynomial. This means that, Argue that is the only solution.
Write the polynomials as vectors in . Row operations will show that this matrix A has 3 pivot positions. So it therefore spans and by the isomorphism between also .
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