https://file.aiquickdraw.com/mathbot/file/1725906965452o6m8e9hm.jpg

The task requires performing a series of row operations on matrices, and we need to apply the operations in the given order.

### Row operations provided:
1. \(-2R_1 + R_2 \rightarrow R_2\)
2. \(-R_1 + R_3 \rightarrow R_3\)
3. \(-\frac{1}{3} R_2 \rightarrow R_2\)
4. \(R_2 + R_3 \rightarrow R_3\)
5. \(\frac{1}{3} R_3 \rightarrow R_3\)

#### To proceed:
1. We start with a matrix (denote it as \(A\)).
2. Apply each operation one by one to change the rows of the matrix.
3. After each operation, we get an updated matrix.

Let's walk through the operations step by step.

#### Initial Matrix
Let the initial matrix be denoted as:
\[
A = \begin{bmatrix}
R_1 \\
R_2 \\
R_3
\end{bmatrix}
\]
Since the exact values of \(R_1\), \(R_2\), and \(R_3\) are not provided in the image, could you please clarify the original matrix values?

Once I have the matrix, I will perform each row operation, updating the matrix at each step.

Would you like me to assume any sample matrix or provide the original matrix if you have it?

Put the matrices in order based on the given row operations: -2R1 + R2 → R2, -R1 + R3 → R3, -1/3R2 → R2, R2 + R3 → R3, 1/3R3 → R3.

Learn how to apply a series of matrix row operations, including row addition, scaling, and replacement. This tutorial will guide you through Gauss-Jordan elimination to manipulate matrices efficiently. Suitable for advanced high school or college students.

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