Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r }
1 & 5 & - 6 & - 9 \
0 & 1 & 2 & - 12 \
0 & 0 & 0 & 6
\end{array} \right]$$ 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

Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r } 
1 & 5 & - 6 & - 9 \
0 & 1 & 2 & - 12 \
0 & 0 & 0 & 6
\end{array} \right]$$ 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 in the augmented matrix where the coefficients of the variables are all zeros but the constant term is non-zero (0, 0, 0 | 6) indicates that the system is inconsistent, meaning it has no solutions.

Suppose That You Are Solving a System of Three Linear [15−6−9012−120006]\left[ \begin{array} { r r r | r } 1 & 5 & - 6 & - 9 \\0 & 1 & 2 & - 12 \\0 & 0 & 0 & 6\end{array} \right]​100​510​−620​−9−126​​

Suppose That You Are Solving a System of Three Linear $\left[ \begin{array} { r r r | r } 1 & 5 & - 6 & - 9 \\0 & 1 & 2 & - 12 \\0 & 0 & 0 & 6\end{array} \right]$