Please anwser the following question.

Given two $3$D coordinate systems, $($:$u,v,w$:$)$ and $($:$p,q,r$:$),$ having the same origin, what is the homogeneous transformation that maps point $x_{pqr}$ in $($:$p,q,r$:$)$ to the corresponding point $x_{\text{u}\text{v}\text{w}}$ in $($:$u,v,w$:$)?$

Note that neither coordinate system above is the canonical $($:$e_1,e_2,e_3$:$)$ system.

In the $44$ matrices below, the vectors $u,v,w,p,q,r$ are laid out in rows or columns and are all written with coordinates in the canonical system.