Solve the given system of equations.
\[
\begin{array}{l}
3 x+5 y-3 z=-1 \\
2 x-5 y+2 z=25 \\
4 x-2 y+4 z=10
\end{array}
\]
Select the correct choice below and fill in any answer boxes within your choice.
A. There is one solution. The solution set is
B. There are infinitely many solutions.
C. There is no solution.
Answer
Final Answer: \(\boxed{x = 4, y = -5, z = -4}\)
Step 1 ：Represent the system of equations in matrix form as follows: \[\begin{bmatrix} 3 & 5 & -3 \\ 2 & -5 & 2 \\ 4 & -2 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -1 \\ 25 \\ 10 \end{bmatrix}\]
Step 2 ：Solve the system of equations using the matrix method. The solution is \(x = 4\), \(y = -5\), \(z = -4\).
Step 3 ：Since the system of equations has a unique solution, we conclude that there is one solution.
Step 4 ：Final Answer: \(\boxed{x = 4, y = -5, z = -4}\)
