Solve the problem.
-Find the general solution of the homogeneous system below. Give your answer as a vector. $$\begin{array} { r }
x _ { 1 } + 2 x _ { 2 } - 3 x _ { 3 } = 0 \
4 x _ { 1 } + 7 x _ { 2 } - 9 x _ { 3 } = 0 \
- x _ { 1 } - 4 x _ { 2 } + 9 x _ { 3 } = 0
\end{array}$$
A)
$$\left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = x _ { 3 } \left[ \begin{array} { r }
3 \
- 3 \
1
\end{array} \right]$$
B)
$$\left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { r }
- 3 \
3 \
1
\end{array} \right]$$
C)
$$\left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = x _ { 3 } \left[ \begin{array} { r }
- 3 \
3 \
1
\end{array} \right]$$
D)
$$\left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = x _ { 3 } \left[ \begin{array} { r }
- 3 \
3 \
0
\end{array} \right]$$

Question

Solve the problem.
-Find the general solution of the homogeneous system below. Give your answer as a vector. $$\begin{array} { r } 
x _ { 1 } + 2 x _ { 2 } - 3 x _ { 3 } = 0 \
4 x _ { 1 } + 7 x _ { 2 } - 9 x _ { 3 } = 0 \
- x _ { 1 } - 4 x _ { 2 } + 9 x _ { 3 } = 0
\end{array}$$
A)
$$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = x _ { 3 } \left[ \begin{array} { r } 
3 \
- 3 \
1
\end{array} \right]$$
B)
$$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = \left[ \begin{array} { r } 
- 3 \
3 \
1
\end{array} \right]$$
C)
$$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = x _ { 3 } \left[ \begin{array} { r } 
- 3 \
3 \
1
\end{array} \right]$$
D)
$$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 }
\end{array} \right] = x _ { 3 } \left[ \begin{array} { r } 
- 3 \
3 \
0
\end{array} \right]$$

Quizplus · Accepted Answer

The system of equations can be solved using Gaussian elimination or matrix methods to find the general solution. The solution is a vector that is a scalar multiple of $[-3, 3, 1]$, which corresponds to option C.

Solve the Problem A) B) [x1x2x3]=[−331]\left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { r } - 3 \\3 \\1\end{array} \right]​x1​x2​x3​​​=​−331​​

Solve the Problem A) B) $\left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { r } - 3 \\3 \\1\end{array} \right]$