Provide an appropriate response.
-Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix.
$$\left[ \begin{array} { r r r | r }
1 & 7 & 18 & 24 \
0 & 0 & 0 & 0 \
0 & 6 & 5 & - 25
\end{array} \right]$$
What conclusion can you draw about the solutions of the system?
A) The system has infinitely many solutions.
B) The system has exactly one solution.
C) The system has no solutions.
D) There is not enough information to draw any conclusion about the solutions of the system.

Question

Provide an appropriate response.
-Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix.
$$\left[ \begin{array} { r r r | r } 
1 & 7 & 18 & 24 \
0 & 0 & 0 & 0 \
0 & 6 & 5 & - 25
\end{array} \right]$$
What conclusion can you draw about the solutions of the system?
A) The system has infinitely many solutions.
B) The system has exactly one solution.
C) The system has no solutions.
D) There is not enough information to draw any conclusion about the solutions of the system.

Quizplus · Accepted Answer

The presence of a row of zeros (second row) in the augmented matrix indicates that the system is dependent, which means there are infinitely many solutions. This is because the row of zeros does not affect the solution set, and the remaining equations are not contradictory.

Provide an Appropriate Response [1718240000065−25]\left[ \begin{array} { r r r | r } 1 & 7 & 18 & 24 \\0 & 0 & 0 & 0 \\0 & 6 & 5 & - 25\end{array} \right]​100​706​1805​240−25​​

Provide an Appropriate Response $\left[ \begin{array} { r r r | r } 1 & 7 & 18 & 24 \\0 & 0 & 0 & 0 \\0 & 6 & 5 & - 25\end{array} \right]$