QuestionConsider the following vectors: $$\mathbf{a}=\left[\begin{array}{c} 1 \\ 2 \\ -3 \\ -1 \end{array}\right] \quad \mathbf{b}=\left[\begin{array}{c} 1 \\ 4 \\ -1 \\ -2 \end{array}\right] \mathbf{c}=\left[\begin{array}{c} 2 \\ -2 \\ -10 \\ -1 \end{array}\right]$$
For each of the following vectors, determine whether it is in $\operatorname{span}\{\mathbf{a}, \mathbf{b}, \mathbf{c}\}$. If so, express it as a linear combination using $a, b$, and $c$ as the names of the vectors above. $\mathbf{v}_{1}=\left[\begin{array}{c}2 \\ -4 \\ -12 \\ 0\end{array}\right]$ < Select an answer > $\mathbf{v}_{2}=\left[\begin{array}{c}-2 \\ -8 \\ 2 \\ 4\end{array}\right] \quad$ Select an answer > $\mathbf{v}_{3}=\left[\begin{array}{c}-10 \\ 2 \\ 6 \\ -6\end{array}\right]$ < Select an answer >