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## Homework Statement

Think of the following matrix

[itex]

A =

\left( \begin{array}{ccc}

a & b & c \\

d & e & f \\

g & h & i \end{array} \right)

[/itex]

as a transformatiom of [itex]\mathbb{R}^3[/itex] onto itself. Describe [itex]A[/itex] 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 [itex]A[/itex] as a product [itex]A = BC[/itex] where [itex]B[/itex] and [itex]C[/itex] are 3-by-3 matrices, [itex]B[/itex] representing a projection onto a plane and [itex]C[/itex] representing a shearing of such plane.

Since [itex]B[/itex] is a projection it must be that [itex]B = B^2[/itex] 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 [itex]C[/itex]. How do we proceed after that?

Any help is greatly appreciated :D