(adsbygoogle = window.adsbygoogle || []).push({}); 1) Let U be a plane through the origin in R^3 with a nonzero normal vector n=[a b c]^T. Find the projection matrix of X=[x1 x2 x3]^T onto U.

I got this question from my linear algebra test today and I am dying on it.

I tried something out but ended up with a terribly ugly result in which I have no confidence of it being right.

My method:

Since (projection of X onto n) gives the perpendicular (closeest) distance from X to the plane U, I have the following inequality: (in orthongonal complement of U)

(projection of X onto n) = X - (projection of X onto U)(<-is this right?)

and then solve for (projection of X onto U) for which I can obtain the induced matrix by factoring the matrix [x1 x2 x3]^T out

and this ends up with some ugly calculations (this question only worth 5 marks, how can I take that long?)

Is there a flaw in this thinking? Is it right?

I seriously think I have missed something...Is there a very easy method to do this question? Can someone teach me? I can't sleep without it.

Thanks a lot!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Matrix Transformation ugly problem

**Physics Forums | Science Articles, Homework Help, Discussion**