Suppose that you are solving a system of three linear equations by the row echelon method and obtain the follon augmented matrix.
$$\left[ \begin{array} { r r r r }
1 & - 8 & 4 & 17 \
0 & 1 & 2 & 10 \
0 & 0 & 0 & 12
\end{array} \right]$$
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.
$$\left[ \begin{array} { r r r r } 
1 & - 8 & 4 & 17 \
0 & 1 & 2 & 10 \
0 & 0 & 0 & 12
\end{array} \right]$$
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 third row of the matrix, [0 0 0 12], indicates an equation 0x + 0y + 0z = 12, which is a contradiction (0 ≠ 12), meaning the system has no solutions.

Suppose That You Are Solving a System of Three Linear [1−84170121000012]\left[ \begin{array} { r r r r } 1 & - 8 & 4 & 17 \\0 & 1 & 2 & 10 \\0 & 0 & 0 & 12\end{array} \right]​100​−810​420​171012​​

Suppose That You Are Solving a System of Three Linear $\left[ \begin{array} { r r r r } 1 & - 8 & 4 & 17 \\0 & 1 & 2 & 10 \\0 & 0 & 0 & 12\end{array} \right]$