(Solved): The reduced row echelon form of a system of linear equations is given. Write the system of equation ...

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use \( w, x, y, z \) as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. A. B. C. D. \[ \left\{\begin{array}{rr} w+z= & -4 \\ x+2 z= & 3 \\ y-z= & 0 \\ z= & 0 \end{array}\right. \] \[ \left\{\begin{array}{rr} w+z= & -4 \\ x+2 z= & 3 \\ y-z= & 0 \\ 0 & =0 \end{array}\right. \] \[ \begin{array}{l} \left\{\begin{array}{l} w=-4 \\ x=-3 \\ y=0 \\ z=0 \end{array}\right. \\ {\left[\begin{array}{rrrr|r} 1 & 0 & 0 & 1 & -4 \\ 0 & 1 & 0 & 2 & 3 \\ 0 & 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]} \\ \end{array} \] Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The system is consistent. The solution is (Simplify your answers.) B. The system is consistent. There are infinitely many solutions. The solution can be written as \( \{(w, x, y, z) \mid w=x= \) and \( y=z \) is any real number \( \} \). (Simplify your answer. Type expressions using \( z \) as the variable.) C. The system is consistent. There are infinitely many solutions. The solution can be written as \( \{(w, x, y, z) \mid w=\quad x= \) and \( y \) is any real number, \( z \) is any real number \( \} \).