Which matrix shown below indicates that the equations of its associated system are dependent?
A) $\left[ \begin{array} { c c | c }
1 & 6 & - 7 \
0 & 3 & 0
\end{array} \right]$
B) $\left[ \begin{array} { c c | c }
1 & 6 & - 7 \
0 & 0 & 5
\end{array} \right]$
C) $\left[ \begin{array} { c c | c }
1 & 6 & - 7 \
0 & 8 & 0
\end{array} \right]$
D) $\left[ \begin{array} { c c | c }
1 & 6 & - 7 \
0 & 8 & 5
\end{array} \right]$
E) $\left[ \begin{array} { c c | c }
1 & 6 & - 7 \
0 & 0 & 0
\end{array} \right]$

Question

Which matrix shown below indicates that the equations of its associated system are dependent?
A) $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 3 & 0
\end{array} \right]$
B) $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 0 & 5
\end{array} \right]$
C) $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 8 & 0
\end{array} \right]$
D) $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 8 & 5
\end{array} \right]$
E) $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 0 & 0
\end{array} \right]$

Quizplus · Accepted Answer

A matrix representing a system of equations will indicate dependent equations if it has a row of all zeros or a row that is a scalar multiple of another row. In this case, the matrix in choice E has a row of all zeros, indicating that one of the equations is dependent on the other.

Which Matrix Shown Below Indicates That the Equations of Its [16−7030]\left[ \begin{array} { c c | c } 1 & 6 & - 7 \\0 & 3 & 0\end{array} \right][10​63​−70​]

Which Matrix Shown Below Indicates That the Equations of Its $\left[ \begin{array} { c c | c } 1 & 6 & - 7 \\0 & 3 & 0\end{array} \right]$