Use the matrix capabilities of a graphing utility to reduce the augmented matrix corresponding to the system of equations,and solve the system. $$\left\{ \begin{aligned}
x + 2 y + 2 z + 4 w & = 20 \
3 x + 6 y + 5 z + 12 w & = 53 \
x + 3 y - 3 z + 2 w & = - 18 \
6 x - y - z + w & = - 30
\end{aligned} \right.$$
A)(-4,1,7,-2)
B)(-4,-1,7,2)
C)(-4,1,-7,2)
D)(-4,-1,-7,-2)
E)(-4,1,7,2)

Question

Use the matrix capabilities of a graphing utility to reduce the augmented matrix corresponding to the system of equations,and solve the system.​ $$\left\{ \begin{aligned}
x + 2 y + 2 z + 4 w & = 20 \
3 x + 6 y + 5 z + 12 w & = 53 \
x + 3 y - 3 z + 2 w & = - 18 \
6 x - y - z + w & = - 30
\end{aligned} \right.$$ ​
A)​(-4,1,7,-2)
B)(-4,-1,7,2)
C)(-4,1,-7,2)
D)(-4,-1,-7,-2)
E)(-4,1,7,2)

Quizplus · Accepted Answer

The correct answer is E.The augmented matrix corresponding to the system of equations is:$$\left[ \begin{array}{cccc|c} 1 & 2 & 2 & 4 & 20 \\ 3 & 6 & 5 & 12 & 53 \\ 1 & 3 & -3 & 2 & -18 \\ 6 & -1 & -1 & 1 & -30 \end{array} ight]$$Using a graphing utility, we can reduce the augmented matrix to:$$\left[ \begin{array}{cccc|c} 1 & 0 & 0 & 0 & -4 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 7 \\ 0 & 0 & 0 & 1 & 2 \end{array} ight]$$Therefore, the solution to the system of equations is:$$x = -4, y = 1, z = 7, w = 2$$

Use the Matrix Capabilities of a Graphing Utility to Reduce