Express 3x3 matrix as projection + shearing

[TomAlso]

Homework Statement

Think of the following matrix

<br /> A = <br /> \left( \begin{array}{ccc}<br /> a &amp; b &amp; c \\<br /> d &amp; e &amp; f \\<br /> g &amp; h &amp; i \end{array} \right)<br />

as a transformatiom of \mathbb{R}^3 onto itself. Describe A as a projection onto a plane followed by a shearing motion of the plane.

2. The attempt at a solution

So the problem basically asks to rewrite A as a product A = BC where B and C are 3-by-3 matrices, B representing a projection onto a plane and C representing a shearing of such plane.

Since B is a projection it must be that B = B^2 and that is pretty much all I know. I can't seem to find precise definition of shearing as a transformation. What can we say about C. How do we proceed after that?

Any help is greatly appreciated :D

 

[alanlu]

http://en.wikipedia.org/wiki/Shear_mapping

 

[kai_sikorski]

Im confused about how this could be true for a non-singular matrix, since all vectors in R³ seem to get mapped to 1 plane..

 

[kai_sikorski]

EDIT: never mind this was wrong