It looks like you're performing a row operation on a matrix, specifically using elementary row operations that involve linear combinations of the rows. The operation you described is:

\[
R2 = 2R1 - R1
\]

To clarify, this operation means that you are updating the second row (\(R2\)) by subtracting the first row (\(R1\)) from two times the first row (\(2R1\)). This simplifies to:

\[
R2 = R1
\]

### Step-by-Step Explanation

1. **Original Matrix Row Setup:** Let's assume you have a matrix where the first row is represented by \(R1\) and the second row is represented by \(R2\).

2. **Applying the Operation:** When you apply \(R2 = 2R1 - R1\), you are essentially calculating:

   \[
   R2 = (2 \cdot R1) - R1 = R1
   \]

   So, the new second row (\(R2\)) will be identical to the first row (\(R1\)).

3. **Result of the Operation:** After performing this operation, the matrix's second row will have the same entries as the first row.

Would you like more details on row operations or a specific example using a matrix?  

### Related Questions
1. What are elementary row operations in linear algebra?
2. How do row operations help in solving systems of linear equations?
3. What is the effect of row swapping on a matrix's determinant?
4. How can you use row reduction to find the inverse of a matrix?
5. What does it mean for a matrix to be in row echelon form?

### Tip
Remember that row operations are crucial in matrix methods for solving systems of linear equations, such as Gaussian elimination and finding determinants.

Explore the row operation R2 = 2R1 - R1 in the context of linear algebra. This guide provides a clear explanation of matrix row operations, highlighting key concepts and theorems involved in matrix manipulation. Ideal for college-level students studying linear algebra.

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