Problem
Write the system of equations associated with the given augmented matrix. Do not solve. \[ \left[\begin{array}{ccc|c} 4 & 2 & 1 & 4 \\ 0 & 2 & 5 & 16 \\ -1 & 3 & 5 & 11 \end{array}\right] \] Choose the correct answer below. A. \[ \begin{array}{r} 4 x+2 y+z=4 \\ 2 y+5 z=16 \\ -x+3 y+5 z=11 \end{array} \] B. \[ \begin{aligned} 4 x+2 y+z & =4 \\ x+2 y+5 z & =11 \\ -x+3 y+5 z & =16 \end{aligned} \] C. \[ \begin{aligned} 4 x+2 y+z & =16 \\ 2 y+5 z & =4 \\ -x+3 y+5 z & =11 \end{aligned} \] D. \[ \begin{aligned} 4 x-z & =4 \\ 2 x+2 y+3 z & =16 \\ x+5 y+5 z & =11 \end{aligned} \]
Solution
Step 1 ：Write the system of equations associated with the given augmented matrix. Do not solve.
Step 2 ：\[\begin{array}{r} 4 x+2 y+z=4 \\ 2 y+5 z=16 \\ -x+3 y+5 z=11 \end{array}\]
Step 3 ：The correct answer is A. The system of equations associated with the given augmented matrix is:
Step 4 ：\[\boxed{\begin{array}{r} 4 x+2 y+z=4 \\ 2 y+5 z=16 \\ -x+3 y+5 z=11 \end{array}}\]
