Brendan's questions

[brendan]

Find the matrix of the transformation T which orthogonally project a point (x,y,z) onto the plane x + y + z = 0.

[brendan]

anyone? 

[brendan]

nvm i solved it

Now for another one:

Prove that for an invertible matrix is an eigenvalue of if and only if is an eigenvalue of What relationship holds between the eigenvectors of  and 

I'm not sure abt the stuff in red

[phagist_]

The eigenvalue of smallest magnitude of a matrix is the same as the reciprocal of the largest eigenvalue of the inverse of the matrix.

Not sure if that is what they're after, though.

[brendan]

Let , otherwise

Show that at

[enwiabe]

fix up the tex plz

[brendan]

oh nvm i solved it

[enwiabe]

Um, evaluate partialdf/dx then partialdf/dy. Then take both limits when x -> 0 and y -> 0... show that both limits are equal to 0.

Tada. Are you having trouble evaluating the partial derivatives f_x and f_y? If so, remember it's a pretty involved product/quotient rule qu.

[enwiabe]

k cool

[brendan]

i used first principles

[enwiabe]

that must've taken you a while. Multi-variable first-principles are a bitch