这是一份oxford牛津大学作业代写的成功案例
If $t$ is a transformation represented by
$$
\operatorname{Rep}{B, D}(t)=\left(\begin{array}{ll} 1 & 0 \ 1 & 1 \end{array}\right){B, D} \quad \text { so that } \vec{v}=\left(\begin{array}{c}
v_{1} \
v_{2}
\end{array}\right){B} \mapsto\left(\begin{array}{c} v{1} \
v_{1}+v_{2}
\end{array}\right)_{D}=t(\vec{v})
$$
then the scalar multiple map $5 t$ acts in this way.
$$
\vec{v}=\left(\begin{array}{l}
v_{1} \
v_{2}
\end{array}\right){B} \longmapsto\left(\begin{array}{c} 5 v{1} \
5 v_{1}+5 v_{2}
\end{array}\right){D}=5 \cdot t(\vec{v}) $$ Therefore, this is the matrix representing $5 t$. $$ \operatorname{Rep}{B, D}(5 t)=\left(\begin{array}{ll}
5 & 0 \
5 & 5
\end{array}\right)_{B, D}
$$
Oxford COURSE NOTES ：
The elementary reduction matrices are obtained from identity matrices with one Gaussian operation. We denote them:
(1) $I \stackrel{k \rho_{i}}{\longrightarrow} M_{i}(k)$ for $k \neq 0$;
(2) $I \stackrel{\rho_{i} \leftrightarrow \rho_{j}}{\longrightarrow} P_{i, j}$ for $i \neq j$;
(3) $I \stackrel{k \rho_{i}+\rho_{j}}{\longrightarrow} C_{i, j}(k)$ for $i \neq j$.