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    Kernel and image

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    Let V=W= T^3 and let T: V-> W be the projection onto the xy plane sending (x,y,z) to (x,y,o).
    (a)determine the kernel of T (b)determine the image of T (c)...
    (See attachment for full question)

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    Solution Preview

    Please see the attachment.

    Problem #1
    , is a projection with
    (1) For any , we have , so we get . Thus the kernel of is
    (2) The image of is
    (3) Let , ...

    Solution Summary

    This shows how to determine the kernel and image of a given projection.