The Matrix Is the Reduced Echelon Matrix for a System $$\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 10 & - 8 \\0 & 1 & 0 & 0 & 5 \\0 & 0 & 1 & 6 & 3 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

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. $$\left[ \begin{array} { r r r r | r } 1 & 0 & 0 & 10 & - 8 \\0 & 1 & 0 & 0 & 5 \\0 & 0 & 1 & 6 & 3 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

A) ( $-$ 8 $-$ 10 k , 5, 3 $-$ 6 k , k ) , where k is any real number
B) ( $-$ 8 $-$ 10 k , 5, 3 + 6 k , k ) , where k is any real number
C) ( $-$ 8 + 10 k , 5, 3 $-$ 6 k , k ) , where k is any real number
D) ( $-$ 8 + 10 k , 5, 3 + 6 k , k ) , where k is any real number
E) inconsistent