Thread: Linear projection problem

One more problem found - please help if you can:

The linear projection f is set with (2,1) -> (2,1,1) (1,1) -> (1,-1,2). Find the matrix that fits this linear projection in relation to the standard base, his formula and his core (subspace of all domain elements that project in the zero of the codomain).

tnx

So we know that



and



Now we have a system of equations for the transformation of the basis vectors

So if we subtract the 2nd equation from the first we get



subbing into either equation gives



Now these are the columns of the transformation matrix.