Equivalence classes for an particular relation question

[LHS]

Homework Statement

[PLAIN]http://img15.imageshack.us/img15/1/unledjs.png

Homework Equations

The Attempt at a Solution

Hi,

If anyone could help me with this I would be very glad! I have said that M=(aij) and M^T=M^-1
therefore if e1 relates v, where v=(x,y,z) then v=(a11,a21,a31) and all of those values can't be simultaneously zero for M^-1 to exist.. can't seem to get any further!

 

[micromass]

So, you'll have to determine what \{Me_1~\vert~M~\text{orthogonal}\} is. Now, do you know what \|Me_1\| is (= the norm of Me_1)??