Perform the indicated Row Operation. SWAP R 1 ↔ R 2 R_1\leftrightarrow R_2 R 1 ↔ R 2

Everyone. So let's take a look at this practice problem. Hopefully, you had a chance to work it out on your own. It's pretty straightforward. We're just gonna take this matrix that we have over here, and we have to indicate or we have to perform the indicated row operation. Remember, row operations like, swapping or adding or multiplying are really just ways to manipulate the rows of a matrix. Alright? So in this case, what we're gonna do is we're gonna swap r 1 and r 2. Remember, these really just mean the rows. This little notation here means that this is row 1 and this is gonna be row 2. Really, all we have to do is just sort of manipulate this matrix and flip these 2 rows. So now row 2 becomes row 1 and then row 1 becomes row 2. So what we can do here is we can when when we rewrite the other matrix for the last column, for the last row that you have over here, this just could remains just completely unaffected. Nothing happens to row 3. So in the words, you can just repeat these numbers, 2, 0, 5, and 2. Nothing happens to those. What happens to the first two rows though is that they just get swapped. So what happens is that the 7, 9, 3, and 4 just goes now to the bottom. It will go down here, And so this will become 7, 9, 3, and 4. And then the 1843 will just sort of flip over to the top. So it'd be 1, 8, 4, and 3. Alright? So that's what these row operations are just doing. They're sort of you know, there's sometimes you will have to change 2 of the rows. Sometimes it'll only just affect 1 of the rows. Alright? So hopefully that made sense. Thanks for watching.

7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

Struggling with College Algebra?

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Multiple Choice

Perform the indicated Row Operation.

SWAP $R_1\leftrightarrow R_2$

Matrix showing a system of equations for row operation: swap R1 and R2.

Matrix

Verified step by step guidance

Identify the rows that need to be swapped. In this case, we need to swap Row 1 (R1) and Row 2 (R2).

Write down the original matrix before the swap. The matrix is: \[ \begin{bmatrix} 7 & 9 & 3 & | & 4 \\ 1 & 8 & 4 & | & 3 \\ 2 & 0 & 5 & | & 2 \end{bmatrix} \]

Perform the swap operation by exchanging the positions of Row 1 and Row 2. After swapping, Row 1 becomes Row 2 and vice versa.

Write down the new matrix after the swap. The matrix is now: \[ \begin{bmatrix} 1 & 8 & 4 & | & 3 \\ 7 & 9 & 3 & | & 4 \\ 2 & 0 & 5 & | & 2 \end{bmatrix} \]

Verify the swap by checking that the elements of the original Row 1 are now in Row 2 and the elements of the original Row 2 are now in Row 1.