Perform the indicated Row Operation. ADD R 1 + 2 ⋅ R 3 → R 1 R_1+2\cdot R_3\rightarrow R_1 R 1 + 2 ⋅ R 3 → R 1

Welcome back, everyone. So let's get some more practice with row operations. I've got this 3 by 4 matrix with 3 rows, 4 columns, and I'm gonna perform the indicated row operation here. Let's take a look. It says that what I'm gonna do is I'm gonna take row 1, and I'm gonna add it to 2 times row 3, and that will become my new r one. So remember, the little r's and big r just kind of mean the new versus old or old versus new. So these are just the old rows, r one, r two, r three. They're all lowercase. And I'm gonna do something to them, and eventually, I'll get another matrix, my new matrix, in which this is gonna be my big r one and then so on and so forth. Alright? So let's take a look here. It says what I'm gonna do is I'm gonna take all the numbers that are in r one, this first row here, and I'm gonna add them to a multiple of row 3, which is 2 times row 3, and that will become my new r one. Now one of the things to remember about these types of row operations is that this will only affect row 1, which means that the other two rows will be completely unaffected in your new matrix. This makes things a little bit easier because, really, you can just literally copy this stuff over. These 2 rows, rows 2 and 3, won't change. So this will still be 5312, and this will still be 1233. Really, all we have to do is just figure out what are the four numbers that are gonna go inside of this row. So here's how I like to do this. Right? So we're gonna take r one and add it to 2 times r three. So I'm just gonna sort of copy these over. Right? So this is my r one. This is gonna be 2, 5, 5, 4, and 3. And then 2 times r 3 is gonna be if I take all of these numbers over here and multiply them by 2. So 2 times this number becomes 2, 2 times this number 4 2 becomes 4, 2 times 3 becomes 6, 2 times 3 becomes 6. So it's kind of as as if it was like adding a system of equations. What is r one plus two times r three actually work out to be? So I'm just gonna sort of add these numbers sort of top to bottom, and these numbers will end up being 4, 9, 109. So these four numbers here are gonna be the four numbers that go inside of your new augmented matrix or, sorry, your new matrix. So you kind of just sort of bring these up over again, and that's what's gonna be your new r one. Alright? So these four numbers are gonna be 4, 9, 109. And that's really all there is to it. Alright? Once you're done with that, this new r one over here, big r one, just becomes this. And this would be the answer or the the solution to this row operation. This would be that new matrix. Alright? Hopefully, that made sense. This is how to do these types of addition, problems. Remember, these are actually gonna be the most common ones, so just feel free to keep practicing until you've got it down. Alright. So thanks for watching. I'll see you in the next one.

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.

ADD $R_1+2\cdot R_3\rightarrow R_1$

Matrix

Verified step by step guidance

Identify the row operation to be performed: Add 2 times the third row to the first row.

Multiply each element of the third row by 2. The third row is [1, 2, 3 | 3], so multiplying by 2 gives [2, 4, 6 | 6].

Add the result from step 2 to the first row. The first row is [2, 5, 4 | 3].

Perform the addition for each corresponding element: (2 + 2), (5 + 4), (4 + 6), and (3 + 6).

Replace the first row with the new values obtained from the addition: [4, 9, 10 | 9].

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Struggling with College Algebra?

Perform the indicated Row Operation.ADD R1+2⋅R3→R1R_1+2\cdot R_3\rightarrow R_1R1+2⋅R3→R1

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Introduction to Matrices practice set

Perform the indicated Row Operation.

ADD $R_1+2\cdot R_3\rightarrow R_1$