math 111, linear algebra. pls see attached and show work. thanks!

4. (a) Find the least-squares approximation to the solution of the system of equations: 2x+y=1 xy=1 x+y=2 (b) Let S be the plane passing through the origin 0 and the points U = (2, 1, 1) and V =(1,1,1). Use your answer to (a) to nd the foot F of the perpendicular dropped from W = (1, 1, 2) to S. (c) Check your solution by verifying that the error vector 8 = FW is orthogonal to u and v. 5. Find equations for all the planes that intersect the yaxis at y = 1 and the z-axis at z = 2, and are tan- gent to the sphere (x 2)2 + y2 + 22 = 4-. Do not use calculus