Answer
Consistent
Solution set: $\{(x,y,z)|x=4-4z,y=2-3z,z\text{ any real number}\}$
Work Step by Step
We are given the reduced row echelon form of a system of linear equations:
$\begin{bmatrix}1&0&4&|&4\\0&1&3&|&2\\0&0&0&|&0\end{bmatrix}$
Write the system of equations corresponding to the given matrix:
$\begin{cases}
1x+0y+4z=4\\
0x+1y+3z=2\\
0x+0y+0z=0
\end{cases}$
$\begin{cases}
x+4z=4\\
y+3z=2\\
0=0
\end{cases}$
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 $z$:
$y+3z=2\Rightarrow y=2-3z$
$x+4z=4\Rightarrow x=4-4z$
The solution set is:
$\{(x,y,z)|x=4-4z,y=2-3z,z\text{ any real number}\}$
