im dealing with a question in R3 where U is a subspace containing all vectors (x,y,z) satisfying x - y + 2z = 0.
Im having trouble picturing what U actually looks like geometrically, theses kind of things always seem to confuse me.
I need to describe the orthogonal complement U(perp) of U?
I also want to find the projections onto U and U(perp) of the vector (2, 1, 4)?
Needless to say im completely lost on where to start..
Originally Posted by Tekken
If you really are "completely lost" then the following won't likely help you much and, perhaps, it is now time to think about private lessons and/or going through the material thoroughly.
U is a plane in the real euclidean space (in this case, it is a plane through the origin and thus it is a subspace) , and its orthogonal complement is the subspace of all vectors that are perpendicular to it.
About (orthogonal) projections onto subspace of vectors you may want to read about orthonormal basis and linear projections: this is way too lengthy to describe it here.