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    Vector space and basis

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    Consider the following elements of the vector space P3 of all polynomials of degree less than or equal to 3.

    p(x)= x-1, q(x)=x+x2, r(x)= 1+x2-x3
    Do these three polynomials form a basis for P3?

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    Solution Preview

    We know, a basis in P3 is {1, x, x2, x3}, in another word, any ...

    Solution Summary

    This shows how to determine if polynomials for a bases for P3.