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The image shows a problem involving solving a system of linear equations using the **Gauss elimination method**. Let me walk through what is written:

1. The first part shows that \( x = 2 \), \( y = -1 \), and \( z = 3 \), which is likely either the initial condition or the result to verify later.

2. The system of equations to be solved is written as:
   \[
   \begin{aligned}
   2x_1 + 3x_2 - x_3 &= 5 \\
   4x_1 + 4x_2 - 3x_3 &= 3 \\
   2x_1 - 3x_2 + 2x_3 &= 2
   \end{aligned}
   \]
   This corresponds to a system of 3 equations with 3 unknowns.

3. The matrix representation of the system is given by the augmented matrix:
   \[
   \begin{pmatrix}
   2 & 3 & -1 & | & 5 \\
   4 & 4 & -3 & | & 3 \\
   2 & -3 & 2 & | & 2
   \end{pmatrix}
   \]
   This matrix will be solved using the **Gauss elimination method**. This involves performing row operations to reduce the matrix into row echelon form.

4. There's a row operation \( R_3 \rightarrow R_3 - R_1 \) written, indicating the step taken to eliminate elements in the third row.

Would you like a step-by-step breakdown of how to apply Gaussian elimination to this matrix, or any other specific part explained in more detail?

### 5 Related Questions:
1. What is the difference between Gaussian elimination and Gauss-Jordan elimination?
2. How do you determine when a system of equations has no solution using Gaussian elimination?
3. What are pivot elements, and how are they used in Gaussian elimination?
4. What is the next row operation after \( R_3 \rightarrow R_3 - R_1 \)?
5. Can the Gaussian elimination method be used for systems with dependent equations?

### Tip:
Always perform row swaps if the pivot element is zero to avoid division by zero during the elimination process.

Solve the system of linear equations using the Gauss elimination method.

This page explains how to solve a system of three linear equations using the Gauss elimination method. Follow a step-by-step breakdown of converting a matrix into row echelon form with key row operations. Ideal for advanced algebra students.

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