$($Maximum $10$ points$)$ Answer the following:

Figure $3$: $($Left$)$ Beam for Question $4($a$).($Right$)$ Beam for Question $4($b$).$

$($a$)(5$ points$)$ Consider the propped cantilever beam shown in figure $3($left$).$ Draw the influence line diagram of the support reaction at $B$ as the unit load moves from $A$ to $B$ i$.$e$.x$ varies between $0$ to $L.$

$($b$)(5$ points$)$ Consider the continuous beam $A-B-C$ shown in figure $3($right$).$ The end $A$ is fixed while those at $B$ and $C$ are rollers. In the context of force method, draw two different primary structures corresponding to this beam. For each primary structure, write the corresponding compatibility equations.