Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is
dependent, give the solution.
-$$\left[ \begin{array} { r r r | r }
1 & 0 & 0 & 0 \
0 & 1 & 0 & 0 \
0 & 0 & 0 & - 4
\end{array} \right]$$
A)inconsistent
B)dependent; z = -4
C)dependent; (0, -4)
D)dependent; (0, 0)

Question

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is
dependent, give the solution.
-$$\left[ \begin{array} { r r r | r } 
1 & 0 & 0 & 0 \
0 & 1 & 0 & 0 \
0 & 0 & 0 & - 4
\end{array} \right]$$
A)inconsistent
B)dependent; z = -4
C)dependent; (0, -4)
D)dependent; (0, 0)

Quizplus · Accepted Answer

The system is inconsistent because the last row of the augmented matrix, [0 0 0 | -4], indicates that 0=−4, which is a contradiction and means there is no solution.

Determine Whether the System Corresponding to the Given Augmented Matrix [10000100000−4]\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & - 4\end{array} \right]​100​010​000​00−4​​

Determine Whether the System Corresponding to the Given Augmented Matrix $\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & - 4\end{array} \right]$