The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. \( \left.\begin{array}{llll|l}1 & 0 & 0 & 0 & 1 / 5 \\ \text { A. The system has exactly one solution. The solution is }(\square & 1 & 0 & 0 & 4 \\ 0 & \\ 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 1 & 2\end{array}\right] \) (Type integers or fractions.) B. The system has infinitely many solutions of the form (Type integers or fractions.)

To analyze the given reduced row echelon form of the augmented matrix, we can extract the information about the system of equations it represents. The matrix is: \[ \begin{array}{cccc|c} 1 & 0 & 0 & 0 & \frac{1}{5} \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 1 & 2 \end{array} \] This matrix corresponds to the following system of equations: 1. \( x_1 = \frac{1}{5} \) 2. \( x_2 = 4 \) 3. \( x_3 = 2 \) 4. \( x_4 = 2 \) ### Step 1: Identify the type of solution From the matrix, we can see that each variable \( x_1, x_2, x_3, \) and \( x_4 \) has a unique value assigned to it. This indicates that the system has exactly one solution. ### Step 2: Write the solution The solution to the system can be expressed as: \[ (x_1, x_2, x_3, x_4) = \left(\frac{1}{5}, 4, 2, 2\right) \] ### Conclusion Thus, the correct choice is: **A. The system has exactly one solution. The solution is** \(\left(\frac{1}{5}, 4, 2, 2\right)\).