Consider a matrix
$A=\left[\begin{array}{ccc}
1 & 0 & 2 \\
-1 & 1 & 0 \\
0 & 1 & 2
\end{array}\right]$
Let $\boldsymbol{b}=\left[\begin{array}{l}1 \\ 3 \\ 0\end{array}\right]$ and $\boldsymbol{x}=\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{array}\right]$
The number of solutions to the linear system of equations $\boldsymbol{A} \boldsymbol{x}=\boldsymbol{b}$ is $\_\_\_\_$ .
- $0$
- $1$
- $6$
- infinitely many
