# Kernel and image

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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https://brainmass.com/math/linear-transformation/kernel-image-26809

#### 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.

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