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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)...
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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.