Given and is a subspace,
Find the orthogonal projections of onto both and .
Now, I've already found so I can decompose X into and s.t.
X = Y + Z.
Let Z = a(-6,-3,4,1), a in R.
(I chose to use Z instead of Y since dim(Z)=1, but dim(Y)=3, so fewer inner-products.)
Dotting both sides with (-6,-3,4,1), we get:
So and .
Y = X - Z so
Hope that's right!