Find a vector a, such that:

Y= ( X2 - a'(x1 x3)') and X2, are independent.

The Data:

X~N(mu,sigma) 3 dimensional

mu'=(2,-3,1)

sigma=( 1 1 1

1 3 2

1 2 2 )

I know that X2~N(-3,3) and I found that Y~N(A*mu,A*sigma*A')

Where

A*mu= -2a1-3-a2

A*sigma*A'=2a2^2-a1^2-4a2+3

So I have the 2 distributions, but how do I find a1 & a2, that makes Y and X2 independent ? I think it has something to do with the covariance being zero, but I don't know how to do it, please help....