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

question 4

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.

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