So here we are, given the following argument in Matrix. But we're gonna want to do is write this as a system of linear equations. Since there three columns and the main part of the Matrix, we're going three variables. Let's call those X. Why Anzi? And since there's three rows, they're gonna be three equations. So we conserve. I write this out one X minus three. Why? Plus three z is equal to negative five. That's the first equation. Next we're gonna want take Native four X minus five. Why minus three Z that is equal to native five. Then we're gonna take negative three X minus two. Why? Plus four. Who's he that is gonna be able to sit? That's how we take this argumentative matrix here and right as a system of linear equations here. Next, we're gonna take the same argument it matrix and before some roa perform some role operations on it. So let's indicate this is real. One this is wrote to and this Israel three outperformed the following corroboration off are to this capital are just means that it's going to replace this lower case R once we've done the Operation R two equals four r one plus r to oops, Plus are to So I'm gonna take four copies of Row one Add wrote to and that's going to us. The new row two. We can do that. So four times one is for negative. Three times for this negative. 12 and four times three. It's 12 and then four times native five is native. 20. So now we're gonna take this. We're gonna go. We're gonna add our two, which is negative for now, you five. Now you have three in negative five. So we're gonna add these values together. So that's zero negative. 12 minus five is negative. Seven or negative. 17. Sorry. 12. My history is nine and negative. 20 minus five is negative. 25. So this is gonna give us our new are, too. Someone can read. Write this in here as zero native. 17 9 Negative night. 25 zero native. 17 nine. No, you're 25. So now let's do this same operation with roll three copies of row one. We're gonna add row three, and that's gonna give us the new version of role three. As you can. Kind of see, we're working towards role actual on form, where we have a one here, a multiple one here and a zero here. And I think you're gonna be surprised what happens once we do this last year operation. So let's take it like this. Three. Want Roe ones roll three, Row three. Remember, Capital aren't means that we're just replacing it once we do the operation, it was three roll ones plus R three. So three times one is three. Look, now you have three times three is negative. Nine, three times three is nine and nail it five times three is negative. 50. You remember We're gonna add role three to it. So you don't get negative three native, sick or negative too. And negative four. And then we're going to want to add six. So u three plus 30 negative nine minus two is negative. 11 or nine minus four is five. And now you 15 plus six is night. So now we're going to want to go and take thes values, which is the new are three and put them right in here. Thank you for this. Get for this and get that. And then we can place these values with zero negative, 11 five and nine. That's how we do those tour operations and how we will this augment matrix as this system of equations.