Answer
Consistent
$\{(x,y,z)|x=-2z-1,y=4z-2,z\text{ any real number}\}$
Work Step by Step
We are given the reduced row echelon form of a system of linear equations:
$\begin{bmatrix}1&0&2&|&-1\\0&1&-4&|&-2\\0&0&0&|&0\end{bmatrix}$
Write the system of equations corresponding to the given matrix:
$\begin{cases}
1x+0y+2z=-1\\
0x+1y-4z=-2\\
0x+0y+0z=0
\end{cases}$
$\begin{cases}
x+2z=-1\\
y-4z=-2\\
0=0
\end{cases}$
Because the reduced row echelon form has a row with only zeros, the system is consistent, having infinitely many solutions.
Express $x,y$ in terms of $z$:
$y-4z=-2\Rightarrow y=4z-2$
$x+2z=-1\Rightarrow x=-2z-1$
The solution set is:
$\{(x,y,z)|x=-2z-1,y=4z-2,z\text{ any real number}\}$
