Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r }
1 & - 7 & 9 & 25 \
0 & 0 & 0 & 0 \
0 & - 10 & - 9 & 23
\end{array} \right]$$ What conclusion can you draw about the solutions of the system?
A) The system has exactly one solution.
B) The system has no solutions.
C) The system has infinitely many 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. $$\left[ \begin{array} { r r r | r } 
1 & - 7 & 9 & 25 \
0 & 0 & 0 & 0 \
0 & - 10 & - 9 & 23
\end{array} \right]$$ What conclusion can you draw about the solutions of the system?
A) The system has exactly one solution.
B) The system has no solutions.
C) The system has infinitely many 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 not of full rank, but since there is no row where the coefficients of the variables are all zero while the constant term is non-zero, the system does not have contradictory equations. This means the system has at least one solution, and the lack of full rank (due to dependent equations or variables) suggests that there are infinitely many solutions.

Suppose That You Are Solving a System of Three Linear [1−792500000−10−923]\left[ \begin{array} { r r r | r } 1 & - 7 & 9 & 25 \\0 & 0 & 0 & 0 \\0 & - 10 & - 9 & 23\end{array} \right]​100​−70−10​90−9​25023​​

Suppose That You Are Solving a System of Three Linear $\left[ \begin{array} { r r r | r } 1 & - 7 & 9 & 25 \\0 & 0 & 0 & 0 \\0 & - 10 & - 9 & 23\end{array} \right]$