Write the system of linear equations represented by the augmented matrix. Use x, y, z, and, if necessary, w for the variables. Then use back-substitution to find the solution.
-$\left[ \begin{array} { r r r | r } 1 & \frac { 3 } { 2 } & 1 & \frac { 1 } { 2 } \ 0 & 1 & - \frac { 1 } { 2 } & - 8 \ 0 & 0 & 1 & 4 \end{array} \right]$
A) $\left\{ \left( \frac { 11 } { 2 } , - 6,4 \right) \right\}$
B) $\left\{ \left( \frac { 1 } { 2 } , - 8,4 \right) \right\}$
C) $\left\{ \left( - 3 , - \frac { 17 } { 2 } , 3 \right) \right\}$
D) $\left\{ \left( - \frac { 21 } { 2 } , - 6,4 \right) \right\}$

Question

Quizplus · Accepted Answer

The system of equations represented by the augmented matrix is:1. $x + \frac{3}{2}y + z = \frac{1}{2}$2. $y - \frac{1}{2}z = -8$3. $z = 4$Back-substituting $z = 4$ into equation 2 gives $y = -6$, and substituting $y = -6$ and $z = 4$ into equation 1 gives $x = \frac{11}{2}$. Therefore, the solution is $\left\{ \left( \frac { 11 } { 2 } , - 6,4 \right) \right\}$.

Write the System of Linear Equations Represented by the Augmented