The Matrix Is the Reduced Echelon Matrix for a System $$\left[ \begin{array} { l l l l | r } 1 & 8 & 0 & 0 & 5 \\0 & 0 & 1 & 0 & - 13 \\0 & 0 & 0 & 1 & 5 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

Multiple Choice

The matrix is the reduced echelon matrix for a system with variables x 1 , x 2 , x 3 , and x 4 . Find the solution set of the system. $$\left[ \begin{array} { l l l l | r } 1 & 8 & 0 & 0 & 5 \\0 & 0 & 1 & 0 & - 13 \\0 & 0 & 0 & 1 & 5 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

A) ( k , 5 $-$ 8 k , $-$ 13, 5) , where k is any real number
B) (5 $-$ 8 k , k , $-$ 13, 5) , where k is any real number
C) (5 + 8 k , k , $-$ 13, 5) , where k is any real number
D) ( k , $-$ 5 + 8 k , $-$ 13, 5) , where k is any real number
E) inconsistent