Use Determinants to Identify Inconsistent Systems and Systems with Dependent Equations
-$$\begin{array} { l }
4 x - y + 2 z = 1 \
3 x + 5 y - z = 0 \
- 6 x - 10 y + 2 z = 0
\end{array}$$
A) system contains dependent equations
B) system is inconsistent

Question

Use Determinants to Identify Inconsistent Systems and Systems with Dependent Equations
-$$\begin{array} { l } 
4 x - y + 2 z = 1 \
3 x + 5 y - z = 0 \
- 6 x - 10 y + 2 z = 0
\end{array}$$
A) system contains dependent equations
B) system is inconsistent

Quizplus · Accepted Answer

The system contains dependent equations because the third equation is a multiple of the second equation (-2 times the second equation), indicating dependency among the equations.

Use Determinants to Identify Inconsistent Systems and Systems with Dependent 4x−y+2z=13x+5y−z=0−6x−10y+2z=0\begin{array} { l } 4 x - y + 2 z = 1 \\3 x + 5 y - z = 0 \\- 6 x - 10 y + 2 z = 0\end{array}4x−y+2z=13x+5y−z=0−6x−10y+2z=0​

Use Determinants to Identify Inconsistent Systems and Systems with Dependent $\begin{array} { l } 4 x - y + 2 z = 1 \\3 x + 5 y - z = 0 \\- 6 x - 10 y + 2 z = 0\end{array}$