(Solved): 2. Show that \( \vec{v}=\left(\begin{array}{l}1 \\ 3 \\ 4\end{array}\right) \) is in the span of \ ...

2. Show that \( \vec{v}=\left(\begin{array}{l}1 \\ 3 \\ 4\end{array}\right) \) is in the span of \[ \mathcal{B}=\left\{\left(\begin{array}{l} 3 \\ 1 \\ 4 \end{array}\right),\left(\begin{array}{l} 5 \\ 1 \\ 6 \end{array}\right)\right\} \] and find the coordinates of \( \vec{v} \) under \( \mathcal{B} \). (Note that \( \mathcal{B} \) is linearly independent and therefore forms a basis for span \( \mathcal{B} \) ).