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Math Help - Span vectors

  1. #1
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    Span vectors

    In an example from the book, the polynomials x^2+3x-2 \ , \ 2x^2+5x-3 \ , \ -x^2-4x+4 generate  P_{2}(R) since they are all in the set and each polynomial in  P_{2}(R) is a linear combination of these three.

    What I don't understand is the what is P_{2}(R) and how do you know that all poly in the set are linear combination of these three?

    thank you.
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    In an example from the book, the polynomials x^2+3x-2 \ , \ 2x^2+5x-3 \ , \ -x^2-4x+4 generate  P_{2}(R) since they are all in the set and each polynomial in  P_{2}(R) is a linear combination of these three.

    What I don't understand is the what is P_{2}(R) and how do you know that all poly in the set are linear combination of these three?

    thank you.
    P_2(\mathbb{R}) is the set of all polynomial functions up to degree 2. We can think of a polynomial ax^2+bx+c as \left[ \begin{array}{c}a\\b\\c\end{array} \right]. What you want to prove that that: \left[ \begin{array}{c}1\\3\\-2\end{array} \right] , \left[ \begin{array}{c}2\\5\\-3\end{array} \right], \left[ \begin{array}{c}-1\\-4\\4\end{array}\right] can be used to express any vector as linear combinations of those three vectors.
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