a$.($K$)$ You are told that markers $3-5$ do form the TCS$.$ Marker $4$ is used as the origin. The x$-$axis is directed from marker $4$ towards marker $3.$ The y$-$axis is directed anteriorly and is normal to the x $-$axis and the vector from marker $4$ towards marker $5.$ The z $-$axis is normal to both the x $-$axis and the y $-$axis such that the axes form a right$-$handed basis.

Using the values for the location the markers in the Global Coordinate System. $($GCS$)$ shown in Figure $1,$ please derive the $4\backslash$times $4$ homogeneous transformation matrix that expresses the TCS$\_($shank $)$ with respect to the GCS $,(^($GCS$)$T$^($TCS$\_($stank $)))$ for the conditions shown in Figure $1.$