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    Vectors, Subspaces and Dimensions

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    a) Find a base for the subspace W of spanned by

    What is the dimension of W?

    b) Let

    1) Show that W is a subspace of
    2) Find a base for W
    3) Determine the dimension of W

    c) Let

    1) Determine whether Y is a base for , the vector space of all 2 x 2 matrices.

    d) Find the two values of a for which the vectors:

    are linearly dependent.

    In the case where a=1, express the vector in terms of

    Please see the attached file for the fully formatted problems.

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    Solution Summary

    Vectors, Subspaces and Dimensions are investigated. The solution is detailed and well presented.