Let

Minimize p(x) = 1/2 ||L[x]||2 - (x, f) using
(a) The Euclidean inner products and norms on both R2 and R3
(b) The Euclidean inner product on R2 and the weighted norm ||w|| = ˆšw21 + 2w22 + 3w23 on R3
(c) The inner product given by

on R2 and the Euclidean norm on R3
(d) The inner product given by

on R2 and the weighted norm

on R3.

2 L(x, y)=| and f- x+y -x+3y 0 (3 1) 2-1 -1 2 2 21