Find the closest point or points to b $= (-1,2)^T$ that lie on the line $x + y = 0$ and also find the line $2x + y = 0$.
The question is obviously elementary but I do not know how to set it up properly to find the points. I know for $x + y = 0$ we have a slope of -1 going through the origin and hence the closest point there is $(-\frac32, \frac32)$, but how can I set it up so that I can find that point. Also, I already know how to do it using differentiation, I only want to know how to do it algebraically using $Ax = b$ form.