Solve the Problem $$2 x _ { 1 } - 16 x _ { 2 } + 10 x _ { 3 } = 0$$

Multiple Choice

Solve the problem.
- $$2 x _ { 1 } - 16 x _ { 2 } + 10 x _ { 3 } = 0$$

A) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = 8 \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] + 5 \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right]$ (with $x _ { 2 } , x _ { 3 }$ free)

B) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = x _ { 2 } \left[ \begin{array} { l } 8 \\ 0 \\ 1 \end{array} \right] + x _ { 3 } \left[ \begin{array} { r } - 5 \\ 1 \\ 0 \end{array} \right] \quad$ (with $x _ { 2 } , x _ { 3 }$ free)

C) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = x _ { 2 } \left[ \begin{array} { l } 8 \\ 1 \\ 0 \end{array} \right] + x _ { 3 } \left[ \begin{array} { r } - 5 \\ 0 \\ 1 \end{array} \right] \quad \left( \right.$ with $x _ { 2 } , x _ { 3 }$ free)

D) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = x _ { 2 } \left[ \begin{array} { r } - 8 \\ 1 \\ 0 \end{array} \right] + x _ { 3 } \left[ \begin{array} { l } 5 \\ 0 \\ 1 \end{array} \right] \quad$ (with $x _ { 2 } , x _ { 3 }$ free) Find the general solution of the simple homogeneous "system" below, which consists of a single linear equation. Give your answer as a linear combination of vectors. Let $x _ { 2 }$ and $x _ { 3 }$ be free variables.