Problem
Determine whether the given system of equations has no solution: (b) \[ \left[\begin{array}{ccc:c} 1 & 0 & 0 & -3 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & 2 \end{array}\right] \] The system has no solution. The system has a unique solution. \[ (x, y, z)=(\square, \square, \square) \] The system has infinitely many solution \[ \begin{array}{l} (x, y, z)=(x, \square, \square) \\ (x, y, z)=(\square, y, \square) \\ (x, y, z)=(\square, \square, z) \end{array} \]
Solution
Step 1 ：Determine whether the given system of equations has no solution: \n\[\left[\begin{array}{ccc:c}1 & 0 & 0 & -3 \0 & 1 & 0 & -1 \0 & 0 & 1 & 2\end{array}\right]\
Step 2 ：The system has a unique solution.
Step 3 ：The solution is \[(x, y, z)=(-3, -1, 2)\]
Step 4 ：Final Answer: The system has a unique solution, \[\boxed{(x, y, z)=(-3, -1, 2)}\]
