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:

   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:

   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.