Solve the system. If there is no solution or if there are infinitely many solutions and the system's equations are dependent, so state.
\[
\begin{array}{rr}
10 x-y+2 z= & -3 \\
x+2 y-z= & -9 \\
2 x+2 y-3 z= & -14
\end{array}
\]
Select the correct choice below and fill in any answer boxes within your choice.
A. There is one solution. The solution set is \{ (Simplify your answers.)
B. There are infinitely many solutions.
C. There is no solution.

Step 1 ：We are given a system of linear equations with three variables. The system is as follows: \[\begin{array}{rr} 10 x-y+2 z= & -3 \\ x+2 y-z= & -9 \\ 2 x+2 y-3 z= & -14 \end{array}\]

Step 2 ：We can solve this system using the matrix method. This involves writing the system of equations in matrix form, finding the inverse of the matrix if it exists, and finally multiplying the inverse with the constants to get the solution.

Step 3 ：The matrix form of the system is: \[A = \begin{bmatrix} 10 & -1 & 2 \\ 1 & 2 & -1 \\ 2 & 2 & -3 \end{bmatrix}, b = \begin{bmatrix} -3 \\ -9 \\ -14 \end{bmatrix}\]

Step 4 ：We find the determinant of matrix A. If the determinant is not zero, the system of equations has a unique solution. The determinant of A is -45, which is not zero.

Step 5 ：We can find the solution by multiplying the inverse of A with b. The solution is \[\begin{bmatrix} -1 \\ -3 \\ 2 \end{bmatrix}\]

Step 6 ：\(\boxed{\text{Final Answer: The solution set is } \{ (-1, -3, 2) \}}\)