Determine whether the system is consistent.
-$$\begin{array} { l }
5 x _ { 1 } + 2 x _ { 2 } + x _ { 3 } = - 11 \
2 x _ { 1 } - 3 x _ { 2 } - x _ { 3 } = 17 \
7 x _ { 1 } + x _ { 2 } + 2 x _ { 3 } = - 4
\end{array}$$
A) No
B) Yes

Question

Determine whether the system is consistent.
-$$\begin{array} { l } 
5 x _ { 1 } + 2 x _ { 2 } + x _ { 3 } = - 11 \
2 x _ { 1 } - 3 x _ { 2 } - x _ { 3 } = 17 \
7 x _ { 1 } + x _ { 2 } + 2 x _ { 3 } = - 4
\end{array}$$
A) No
B) Yes

Quizplus · Accepted Answer

To determine if the system is consistent, we can use methods such as Gaussian elimination or calculating the determinant of the coefficient matrix. A system is consistent if it has at least one solution. Without explicitly solving the system, we can note that there are three equations and three unknowns, and there's no immediate contradiction visible in the equations (such as an equation that simplifies to a falsehood like 0=1). Thus, without a contradiction, the system is likely consistent, indicating that it has at least one solution.

Determine Whether the System Is Consistent A) No B) Yes

Determine Whether the System Is Consistent A) No
B) Yes