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    Linear Equation Questions. See attached file for full problem description.

    Let S be the subspace....
    Explain why this linear equation represents a subspace and find a basis for it.
    Clearly explain why this subspace is a plane.
    Find two orthogonal vectors in the plane.
    Make the set you found orthonormal.
    Explain why your set is a basis for the plane.
    Show that the vector...is not in the plane.
    Find the vector in the plane that is the closest to v.

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    Solution Preview

    Please see the attached file.

    (a) Since is the subspace defined by the equation , then is the set of all points that satisfy the equation. We can give a general solution. Let , then we can find two linearly independent solution and . Especially, let , we obtain the basis of . The basis is , ...

    Solution Summary

    This is a set of questions regarding a subspace, vectors, and basis.