Prоblem 1 - True/Fаlse (40 pts) Fоr eаch оf the following questions, indicаte whether they are True or False. (a) The degrees of freedom can be calculated by using Grubler's formula for any system with a finite number of joints. (b) Any holonomic constraint can be written as a Pfaffian form. (c) Consider (R_{sb'},R,R_{sb}in SO(3)) such that (R_{sb'}=R R_{sb}). This implies that the rotational matrix (R) is applied to ({b})-frame along an axis expressed in ({s})-frame. (d) Given a rotational matrix (Rin SO(3)) such that (Rneq I_{3times3}), there exist a unique (omegainmathbb{R}^3) with (||omega||=1) and a unique (thetainmathbb{R}) such that (R=e^{widehat{omega}theta}). (e) Given a differentiable curve (R_{sb}(t)in SO(3)), the spatial angular velocity (omega_s(t)) and the body angular velocity (omega_b(t)) always satisfy (|omega_s(t)|=|omega_b(t)|) for all time (t). (f) Consider a homogeneous representation of a rigid body (T_{sb}in SE(3)) represented bybegin{equation*} T_{sb}=begin{bmatrix} R_{sb} & p_{sb} \ 0_{1times 3} & 1 end{bmatrix}.end{equation*}There exist some (R_{sb}in SO(3)) and (p_{sb}inmathbb{R}^3) such that (T^{-1}=T^top). (g) A rigid body transformation (Tin SE(3)) is identical to some screw motion. (h) For any matrices (Ain se(3)), it holds that (e^Ain SE(3)). (i) Suppose that a twist coordinate of a transformation matrix (Tin SE(3)) is given as the screw axis (S=[0,0,0,-1,0,0]^top) and the scalar (theta=pi). Then, the screw pitch (h=0). (j) If the pitch of a screw motion is finite and non-zero, namely, (0