Preliminaries

Crazy vector space

Let $V^2$ be the vector space of column vectors with two real components with vector addition

$\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right]o+\left[\begin{array}{c}{w}_1\\ w_2\end{array}\right]=\left[\begin{array}{c}{u}_1+w_1+7\\ u_2+w_2+5\end{array}\right]$

and scalar multiplication

$o.\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right]=\left[\begin{array}{c}{u}_1+7-7\\ u_2+5-5\end{array}\right]$

The sets

$B=\{vec(b{)}_1,$vec$(b{)}_2\}=\{\left[\begin{array}{c}2\\ -3\end{array}\right],\left[\begin{array}{c}-3\\ -4\end{array}\right]\}$

and

$D=\{vec(d{)}_1,$vec$(d{)}_2\}=\{\left[\begin{array}{c}-4\\ -4\end{array}\right],\left[\begin{array}{c}-3\\ -4\end{array}\right]\}$

are bases for the vector space.

What is the change of basis from basis $B$ to basis $D?$

$R_{BD}(id)=$