There haven't been any views yet so I doubt anyone cares but I figured it out. The question was in the section of my book called Change of Basis so I did the problem using that, only to find out that a lot cancels and the answer comes out to be the matrix P that I denote above. You have to find two vectors that span V perp so that is a new basis of R^4, but when you apply the linear transformation and the change of basis formula, they cancel out.