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    Computation of Bases of Various Vector Spaces

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    For each of the following vector spaces, give its dimension and a basis.

    (a) the set of all symmetric 4 x 4 matrices,
    (b) the subspace of P3 consisting of those polynomials in P3 whose graphs
    pass through the origin
    (c) the set of all vectors in R3 that are orthogonal to v = (1,2,-1)

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    Solution Preview

    For each of the following vector spaces V, we wish to give its dimensions and find a basis.
    (a) The set of all symmetric matrices.
    Every symmetric matrix can be written in the following form:

    where are arbitrary ...

    Solution Summary

    We compute the basis of three given abstract vector spaces.