Solve the following system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

x + y + z + w=6

2x - y + z = -1

3x + 2y + z - w= 7

x-4y - 4z + 4w = -3

A. The solution is x= ___ y= ___ z= ___ w=____

B. There are infinitely many solutions. The solution can be written as X=___ Y=___ Z=___ and W is any real number

C. There are infinitely many solutions. The solution can be written as X=___ Y=___ andz is any real number, w is any real number

D. There are infinitely many solutions. The solution can be written as X=__ and Y , Z, and W, are any real numbers

E. The system is inconsistent