Answer
Consistent
Solution set: $\{(x_1,x_2,x_3,x_4)|x_1=1,x_2=2-2x_4,x_3=-3x_4,x_4\text{ is any real number}\}$
Work Step by Step
We are given the reduced row echelon form of a system of linear equations:
$\begin{bmatrix}1&0&0&0&|&1\\0&1&0&2&|&2\\0&0&1&3&|&0\end{bmatrix}$
Write the system of equations corresponding to the given matrix:
$\begin{cases}
1x_1+0x_2+0x_3+0x_4=1\\
0x_1+1x_2+0x_3+2x_4=2\\
0x_1+0x_2+1x_3+3x_4=0
\end{cases}$
$\begin{cases}
x_1+x_4=1\\
x_2+2x_4=2\\
x_3+3x_4=0
\end{cases}$
The system is consistent. As the number of equations is less then the number of variables, it has infinitely many solutions. Express $x_1,x_2,x_3$ in terms of $x_4$:
$x_3+3x_4=0\Rightarrow x_3=-3x_4$
$x_2+2x_4=2\Rightarrow x_2=2-2x_4$
$x_1=1$
The solution set is:
$\{(x_1,x_2,x_3,x_4)|x_1=1,x_2=2-2x_4,x_3=-3x_4,x_4\text{ is any real number}\}$
