Determine whether the system is consistent.
-$$\begin{array} { r }
2 x _ { 1 } + x _ { 2 } = 0 \
x _ { 1 } - 3 x _ { 2 } + x _ { 3 } = 0 \
3 x _ { 1 } + x _ { 2 } - x _ { 3 } = 0
\end{array}$$
A) $Y e s$
B) No

Question

Determine whether the system is consistent.
-$$\begin{array} { r } 
2 x _ { 1 } + x _ { 2 } = 0 \
x _ { 1 } - 3 x _ { 2 } + x _ { 3 } = 0 \
3 x _ { 1 } + x _ { 2 } - x _ { 3 } = 0
\end{array}$$
A) $Y e s$
B) No

Quizplus · Accepted Answer

The system is consistent because it has at least one solution. This can be determined by observing that there are three equations and three unknowns, and there is no immediate contradiction among the equations.

Determine Whether the System Is Consistent 2x1+x2=0x1−3x2+x3=03x1+x2−x3=0\begin{array} { r } 2 x _ { 1 } + x _ { 2 } = 0 \\x _ { 1 } - 3 x _ { 2 } + x _ { 3 } = 0 \\3 x _ { 1 } + x _ { 2 } - x _ { 3 } = 0\end{array}2x1​+x2​=0x1​−3x2​+x3​=03x1​+x2​−x3​=0​

Determine Whether the System Is Consistent $\begin{array} { r } 2 x _ { 1 } + x _ { 2 } = 0 \\x _ { 1 } - 3 x _ { 2 } + x _ { 3 } = 0 \\3 x _ { 1 } + x _ { 2 } - x _ { 3 } = 0\end{array}$