Orthogonality & Least Squares · Hard problem

A control system must deliver readings $A\mathbf x = (3,9)$, where $A$ has rows $(1,2,2)$ and $(2,-1,1)$ – two constraints on three actuator commands $x_1,x_2,x_3$, so there are infinitely many solutions. Find the SMALLEST possible value of $\|\mathbf x\|$ (the minimum-energy command).