1. (10 points) This problem tests one's ability to analyze a block diagram and obtain closed loop (CL) transfer functions from it. Given the block diagram: X(8) G Showing all algebraic steps, derive the open loop Yg transfer functions Y(s)/X(s) = ?? and Y(s)/X2(s) = ?? and show that: G G3 Y(s)/X1(s) G3(s) [G1(s) - G2(s)] and Y(s)/X2(s) G4(S) - 1 Y2 X2(8) GA Y(s)