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Consider the system of equationsTl + 412 613 31. = 3 12I.= -5 I3 + I.=[ I2 + I: = 0.Convert this system to augmented matrix form and solve using Gauss-Jordan elimin...

Question

Consider the system of equationsTl + 412 613 31. = 3 12I.= -5 I3 + I.=[ I2 + I: = 0.Convert this system to augmented matrix form and solve using Gauss-Jordan elimination (or explain why no solu- tion exists). Make sure you show all of your steps. by wit- ing out the Inde operations performed the augmented matrixCheck your answr either by using nuzpy to solve the Sys tem in Python, or by hand by performing an appropriate matrix multiplication on your solution (T-I2-I3.T4). Fou use Python then mak

Consider the system of equations Tl + 412 613 31. = 3 12I.= -5 I3 + I.=[ I2 + I: = 0. Convert this system to augmented matrix form and solve using Gauss-Jordan elimination (or explain why no solu- tion exists). Make sure you show all of your steps. by wit- ing out the Inde operations performed the augmented matrix Check your answr either by using nuzpy to solve the Sys tem in Python, or by hand by performing an appropriate matrix multiplication on your solution (T-I2-I3.T4). Fou use Python then make sure you include your code and the output_



Answers

Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand, and others using technology. HINT [See Examples 1-6.] $$ \begin{aligned} x+y+\quad 4 w &=1 \\ 2 x-2 y-3 z+2 w &=-1 \\ 4 y+6 z+w &=4 \\ 3 x+3 y+3 z+7 w &=4 \end{aligned} $$

They said, This is our question number two. As you can see for the attorney in question here, variable aesthetes missing. Right. So here we can write zero eyes right now, right? The augmented metrics for the U. N. System of immigration. Now here coefficient off our s anti. That is three one and do and on the right side. Really won. Now, for the second question here, proficient off Paris anti That is negative to negative one and one Your negative to never 81 1 And on the right side, we hear one of the three for the thorny question Your coefficient of Paris anti that is 40 and two. Your 40 into and on the right said we have negative toe. But this is the moment and metrics. Thank you.

He had been used to find the values off X y. And so first we will find the leader Met. The is a little right Equivalence off X later. Three to minus one. Then do minus three minus four. Line by line from If you find the dominant, it comes to relieve minus 14. Then we will find the Dublin off the X that is attended the first a car with all modern Metis man, A six foot minus 11 fight. So I like to bake a cake, I think. Mina six miners loving fight. Then write remaining Matic see through minus three mark minus one minus four. But so it comes to be minus 28. Then de by in this team The second column off the given methinks through minus 31 can be gentle by minus X minus, lowering fight remaining about it for prey to one. My nothing's minus 11 by then. Minus one minus will save Medicare between being anything as determined. Not be 40 on a, Dees said, is a clerical. Do you need to call on three. There is learn by the 41 but minus six minus nine and fight so three through one through minus three. It really mind? I think my enough learn. But so it's not going, Billy. Minus a default. So by using crime also just fine. I wasn't gonna go the X, but I didn't. What do you think? With minus 28 by minus one thing, which is a good while you could do Did my body, which is a cardio for a group by minus 40 ideally go minus three. That dick with be that party magical Duke minus 84 given it, but minor forbid, which comes to six.

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.

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