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

To solve the system of equations, we can use matrix reduction techniques (such as Gaussian elimination) on the augmented matrix corresponding to the system. After performing these operations (which are not detailed here due to the nature of the question), we find that the solution to the system is $x = -4$, $y = 1$, $z = 7$, and $w = 2$, which corresponds to choice E.

Use the Matrix Capabilities of a Graphing Utility to Reduce