Quiz: Matrix of a Linear Mapping, Similar Matrices

Determine the matrix of the linear operator $\mathit{L}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule{3pt}{0ex}}$with respect to the basis $\mathit{B}=\left\{\stackrel{\mathit{\to }}{{\mathit{v}}_{1}},\phantom{\rule{5px}{0ex}}\stackrel{\mathit{\to }}{{\mathit{v}}_{2}},\phantom{\rule{5px}{0ex}}\stackrel{\mathit{\to }}{{\mathit{v}}_{3}}\right\}\phantom{\rule{3pt}{0ex}}$, where $\mathit{L}\left(\stackrel{\mathit{\to }}{{\mathit{v}}_{1}}\right)=\stackrel{\mathit{\to }}{2{\mathit{v}}_{1}}-3\stackrel{\mathit{\to }}{{\mathit{v}}_{2}}\phantom{\rule{3pt}{0ex}}$, $\mathit{L}\left(\stackrel{\mathit{\to }}{{\mathit{v}}_{2}}\right)=\stackrel{\mathit{\to }}{3{\mathit{v}}_{1}}+4\stackrel{\mathit{\to }}{{\mathit{v}}_{2}}-\stackrel{\mathit{\to }}{{\mathit{v}}_{3}}\phantom{\rule{3pt}{0ex}}$, $\mathit{L}\left(\stackrel{\mathit{\to }}{{\mathit{v}}_{3}}\right)=-\stackrel{\mathit{\to }}{{\mathit{v}}_{1}}+2\stackrel{\mathit{\to }}{{\mathit{v}}_{2}}+6\stackrel{\mathit{\to }}{{\mathit{v}}_{3}}\phantom{\rule{3pt}{0ex}}$

 $\left[\phantom{\rule{0ex}{10ex}}\phantom{\rule{3pt}{0ex}}$ $\right]\phantom{\rule{0ex}{10ex}}\phantom{\rule{3pt}{0ex}}$