Answer
Yes, the statement makes sense.
Work Step by Step
The provided statement makes sense.
Example:
Consider the system of equations:
$\begin{align}
& x+2y=4 \\
& 3x+6y=18
\end{align}$
The augmented matrix is,
$\left[ \begin{matrix}
1 & 2 & 4 \\
3 & 6 & 18 \\
\end{matrix} \right]$
Now we will reduce the matrix into row reduced echelon form by applying row operations.
First apply ${{R}_{2}}\to {{R}_{2}}-3{{R}_{1}}$
$\left[ \begin{matrix}
1 & 2 & 4 \\
0 & 0 & 18 \\
\end{matrix} \right]$
The reduced system of equations is,
$x+2y=4$ .….. (I)
$0=16$ …… (II)
Equation (II) is absurd.
Therefore, the given system has no solution.
Hence, the provided statement makes sense.
