Write the system of equations associated with the augmented matrix. Do not solve. $$ \left[\begin{array}{rrr|r}1 & 0 & 0 & 8 \ 0 & 1 & 0 & -6 \ 0 & 0 & 1 & 10\end{array} ight] $$

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Write the system of equations associated with the augmented matrix. Do not solve. $$ \left[\begin{array}{rrr|r}1 & 0 & 0 & 8 \ 0 & 1 & 0 & -6 \ 0 & 0 & 1 & 10\end{array}ight] $$

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To write the system of equations associated with the given augmented matrix

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

we can interpret each row of the matrix as an equation. The first three columns represent the coefficients of the variables, and the last column represents the constants on the right side of the equations.

Let the variables be $$x_1$$, $$x_2$$, and $$x_3$$. The system of equations can be written as follows:

1. From the first row: 
   $$
   1x_1 + 0x_2 + 0x_3 = 8 \implies x_1 = 8
   $$

2. From the second row: 
   $$
   0x_1 + 1x_2 + 0x_3 = -6 \implies x_2 = -6
   $$

3. From the third row: 
   $$
   0x_1 + 0x_2 + 1x_3 = 10 \implies x_3 = 10
   $$

Thus, the system of equations associated with the augmented matrix is:

$$
\begin{align*}
x_1 & = 8, \
x_2 & = -6, \
x_3 & = 10.
\end{align*}
$$
The system of equations is: $$ \begin{align*} x_1 & = 8, \ x_2 & = -6, \ x_3 & = 10. \end{align*} $$

Write the system of equations associated with the augmented matrix. Do not solve. \( \left[\begin{array}{rrr|r}1 & 0 & 0 & 8 \\ 0 & 1 & 0 & -6 \\ 0 & 0 & 1 & 10\end{array}\right] \)

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