Let $T : R3 → R3$ be a linear transformation which projects vectors onto the plane π with equation $x−y + 2z = 0$. Find a matrix $A$ such that $T = T_A$
I know how to complete the question I just had a quick inquiry. So I know I need to choose two vectors that span the plane and are orthogonal. It is easy to choose vectors that span the plan but is there a quick and easy way to find two vectors that span the plane and are orthogonal without just guessing what possible combination would work? I know that the two vectors in this case are 1 1 0 and 1 -1 -1