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Transformation 6b

In this figure, is a given transformation, is an arbitrary vector, is on a plane perpendicular to , and the endpoint of is on a line parallel to so that for some . Then , , and . Note on moving an arbitrary point in 3D.  Click on the endpoint of , and arrows appear.  Click again and see a different set of arrows.  Four arrows show movement parallel to the -plane.  Two arrows show movement parallel to the axis. 

How does behave "better" when is in the null space of ?