I'm solving this question, but I don't know what it is.
Consider a plane $x - y + z = 0$, and a point $b = (1, 2, 0)^T$
a) Find a basis of this plane, and a basis of orthogonal subspace to this plane.
b) Find the closest point $\hat{b}$ on the plane to b.
c) What is the error between b and $\hat{b}$?
Is this a linear algebra problem? What's a basis of orthogonal subspace and closest point $\hat{b}$? What's the error between b and $\hat{b}$??