Determine whether the system is consistent.
-$$\begin{array} { l }
x _ { 1 } + x _ { 2 } + x _ { 3 } = 7 \
x _ { 1 } - x _ { 2 } + 2 x _ { 3 } = 7 \
5 x _ { 1 } + x _ { 2 } + x _ { 3 } = 11
\end{array}$$
A) $\mathrm { Yes }$
B) $\mathrm { No }$

Question

Determine whether the system is consistent.
-$$\begin{array} { l } 
x _ { 1 } + x _ { 2 } + x _ { 3 } = 7 \
x _ { 1 } - x _ { 2 } + 2 x _ { 3 } = 7 \
5 x _ { 1 } + x _ { 2 } + x _ { 3 } = 11
\end{array}$$
A) $\mathrm { Yes }$
B) $\mathrm { No }$

Quizplus · Accepted Answer

The system is consistent if it has at least one solution. To determine this, we can use methods such as Gaussian elimination or calculating the determinant of the coefficient matrix. Without explicitly solving the system, we can observe that there are three equations and three unknowns, and there's no immediate contradiction among the equations. Thus, it's reasonable to conclude that the system is likely consistent, meaning it has at least one solution.

Determine Whether the System Is Consistent A) Yes\mathrm { Yes }Yes

Determine Whether the System Is Consistent A) $\mathrm { Yes }$