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    vector spaces

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    Briefly explain, which of the following are vector spaces?

    (a) The set of all real symmetric 3x3 matrices.
    (b) The set of all real 3x3 non-singular matrices.
    (c) The set of all real functions f(x) which are continuous for all x.

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    Solution Preview

    (a) The sum of two symmetric matrices and the scalar multiple of a symmetric matrix is again a symmetric matrix. The zero matrix is ...

    Solution Summary

    Vector spaces are clearly evaluated in this solution.