For the matrix
$[A]=\left[\begin{array}{ccc}
1 & -1 & 0 \\
-1 & 2 & -1 \\
0 & -1 & 1
\end{array}\right]$
which of the following statements is/are TRUE?
- $[A]\{x\}=\{b\}$ has a unique solution
- $[A]\{x\}=\{b\}$ does not have a unique solution
- $[A]$ has three linearly independent eigenvectors
- $[A]$ is a positive definite matrix