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The system of linear equations presented is:

\[
7x + y + 9z = 2
\]
\[
5x - 5y - z = 7
\]
\[
x - 5y - 3z = -9
\]

To write the augmented matrix for this system, you arrange the coefficients of \(x\), \(y\), and \(z\) from each equation into a matrix, along with the constants on the right-hand side. The augmented matrix will be in the form:

\[
\begin{bmatrix}
7 & 1 & 9 & | & 2 \\
5 & -5 & -1 & | & 7 \\
1 & -5 & -3 & | & -9
\end{bmatrix}
\]

Thus, the augmented matrix is:

\[
\begin{bmatrix}
7 & 1 & 9 & 2 \\
5 & -5 & -1 & 7 \\
1 & -5 & -3 & -9
\end{bmatrix}
\]

You would enter this into the matrix fields as follows:

- First row: 7, 1, 9, 2
- Second row: 5, -5, -1, 7
- Third row: 1, -5, -3, -9

Do you want further details or explanations? Here are some follow-up questions to deepen understanding:

1. What does it mean for a matrix to be augmented?
2. How would you perform row reduction on this augmented matrix to solve the system?
3. Can a system of linear equations have no solutions, and how does the augmented matrix reveal that?
4. What are the steps to convert this augmented matrix into reduced row echelon form (RREF)?
5. How can augmented matrices be used to identify dependent and independent equations?

**Tip:** Always double-check that the coefficients in your augmented matrix align with their respective variables in each equation.

Write the augmented matrix for the system of linear equations: 7x + y + 9z = 2, 5x - 5y - z = 7, x - 5y - 3z = -9.

Learn how to write the augmented matrix for the system of linear equations 7x + y + 9z = 2, 5x - 5y - z = 7, and x - 5y - 3z = -9. This solution covers matrix representation and basic linear algebra techniques such as row reduction. Suitable for high school and college students.

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