Use the method of Gauss-Jordan elimination (transforming the augmented matrix into reduced echelon form) to solve the given system of equations.
\(3x_1 + x_2 - 3x_3 = 6\
\(2x_1 + 7x_2 + x_3 = -6\
\(2x_1 + 5x_2 = -3\
Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
A. There is a unique solution, \(x_1 = \), \(x_2 = \), and \(x_3 = \).
(Simplify your answers.)
B. There are infinitely many solutions of the form \(x_1 = \), \(x_2 = s\), and \(x_3 = t\), where \(s\) and \(t\) are real numbers.
(Simplify your answers. Use integers or fractions for any numbers in the expressions.)
C. There are infinitely many solutions of the form \(x_1 = \), \(x_2 = \), and \(x_3 = t\), where \(t\) is a real number.
(Simplify your answers. Use integers or fractions for any numbers in the expressions.)