Answer
the linear system is Inconsistent.
Work Step by Step
$\begin{cases}
-x+2y+5z=4\\
x-2z=0\\
4x-2y-11z=2
\end{cases}$
Multiplying Equation 1 by 4 and adding it to Equation 3, results n new Equation 1.
$\begin{cases}
-4x+8y+20z=16\\
4x-2y-11z=2\\
-- -- -- --\\
6y+9z=18
\end{cases}$
Multiplying Equation 2 by $-4$ and adding it to Equation 3, results in new Equation 2.
$\begin{cases}
4x-2y-11z=2\\
-4x+8z=0\\
-- -- -- --\\
-2y-3z=2
\end{cases}$
Multiplying new Equation 2 by 3 and adding it to new Equation 1.
$\begin{cases}
6y+9z=18\\
-6y-9z=6\\
-- -- --\\
0=24
\end{cases}$
Therefore, the linear system is Inconsistent.
