Use the method of Gauss-Jordan elimination (transforming the augmented matrix into reduced echelon form) to solve the given system of linear equations.
w+ x+y+z=1
2w+2x-2y-2z=6
5w-2x+2y+z=-10
w-x+3y+5z = - 13
Select the correct choice below and fill in any answer boxes within your choice.
A. There is a unique solution, w = , x = , y = , and z = .
(Simplify your answers.)
B. There are infinitely many solutions of the form w = , x = , y=s, and z=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 w = , x = , y= , and z = t, where t is a real number.
(Simplify your answers. Use integers or fractions for any numbers in the expressions.)
D. There is no solution.