The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.
-$$\left[ \begin{array} { r r r }
1 & - 5 & - 1 \
0 & 0 & 7
\end{array} \right]$$
A) $( - 1,7 )$
B) $x _ { 1 } = - 1 + 5 x _ { 2 }$
$x _ { 2 }$ is free
C) No solution
D) $x _ { 1 } = - 1 + 5 x _ { 2 }$
$x _ { 2 } = 7$
$x _ { 3 }$ is free

Question

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.
-$$\left[ \begin{array} { r r r } 
1 & - 5 & - 1 \
0 & 0 & 7
\end{array} \right]$$
A) $( - 1,7 )$
B) $x _ { 1 } = - 1 + 5 x _ { 2 }$
$x _ { 2 }$ is free
C) No solution
D) $x _ { 1 } = - 1 + 5 x _ { 2 }$
$x _ { 2 } = 7$
$x _ { 3 }$ is free

Quizplus · Accepted Answer

The second row of the augmented matrix implies $0x_1 + 0x_2 = 7$, which is a contradiction (0 cannot equal 7). Therefore, the system has no solution.

The Augmented Matrix Is Given for a System of Equations [1−5−1007]\left[ \begin{array} { r r r } 1 & - 5 & - 1 \\0 & 0 & 7\end{array} \right][10​−50​−17​]

The Augmented Matrix Is Given for a System of Equations $\left[ \begin{array} { r r r } 1 & - 5 & - 1 \\0 & 0 & 7\end{array} \right]$