Suppose that you are solving a system of three linear equations by the row echelon method and obtain the follon augmented matrix.
$$\left[ \begin{array} { r r r r }
1 & 17 & 11 & 13 \
0 & 0 & 0 & 0 \
0 & - 18 & 5 & 3
\end{array} \right]$$
What conclusion can you draw about the solutions of the system?
A) There is not enough information to draw any conclusion about the solutions of the system.
B) The system has infinitely many solutions.
C) The system has exactly one solution.
D) The system has no solutions.

Question

Suppose that you are solving a system of three linear equations by the row echelon method and obtain the follon augmented matrix.
$$\left[ \begin{array} { r r r r } 
1 & 17 & 11 & 13 \
0 & 0 & 0 & 0 \
0 & - 18 & 5 & 3
\end{array} \right]$$
What conclusion can you draw about the solutions of the system?
A) There is not enough information to draw any conclusion about the solutions of the system.
B) The system has infinitely many solutions.
C) The system has exactly one solution.
D) The system has no solutions.

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 and the constant term is non-zero, the system does not have a contradiction. Therefore, it has infinitely many solutions.

Suppose That You Are Solving a System of Three Linear [117111300000−1853]\left[ \begin{array} { r r r r } 1 & 17 & 11 & 13 \\0 & 0 & 0 & 0 \\0 & - 18 & 5 & 3\end{array} \right]​100​170−18​1105​1303​​

Suppose That You Are Solving a System of Three Linear $\left[ \begin{array} { r r r r } 1 & 17 & 11 & 13 \\0 & 0 & 0 & 0 \\0 & - 18 & 5 & 3\end{array} \right]$