5

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Question

Exe: z fantle Fcurdina :79 2d airea € itz nEA 22: Man 4-du7gl22icihe ~zrier: JegizeQipa inteper {ecicslounded ine ha3restJenitnzzded ))(Jound3ete5 Degizneed2r ;(Rolnd io ire nzsres: Degrzz022u25 _

Exe: z fantle Fcurdina :79 2d airea € itz nEA 22: Man 4-du7gl22icihe ~zrier: Jegize Qipa inteper {ecicslounded ine ha3restJenit nzzded )) (Jound 3ete5 Degiz need2r ; (Rolnd io ire nzsres: Degrzz 022u25 _



Answers

$$\left\{\begin{array}{rr} -2 x-y-z= & 5 \\ x+y+z= & 0 \\ 3 x+2 y+7 z= & -8 \end{array}\right.$$

For this quest. They give us a system of three equations and they want to straight from Ah, in augmented me Coming up three x for minus for wine. See the hair of that equation around the 1st 1 is actually two eggs, plus why pussy is equal to three. Okay, the second equation. ISS three X minus four away plus two z Whose ego It's a negative seven and the third equation is X plus y plus C cools to and all right. This is an augmented three by three matrix well up to 31 The first call second column all the coalition's for Why one negative one and our third column while dizzy coefficients 1 to 1. And then the column augmented all the values from right three negative seven to

It's already converting from spherical two rectangular. So it's important to note that there is a conversion for this, we're gonna have X equals row, which right is p sign fee code saying there you go. And then why is going to equal rho times sine fee signed data and then z is going to equal roco saying feet. So we're going to use these equations to answer all of our other equations with the given points. So for example, if we're given 45 or six power before there is just an example but we can see this with any problem that's given to us. We would end up having x equals four times the sign of number four which is route 2/2. I'm the code sign pi over six Which is going to be route three over to. That's going to end up giving us route six as we sit here. And then why is going to be four Times The sine of fee? Again, that's going to be rude to over two and then we're going to have times sine of data which is going to be one half. So really that's just gonna end up being rude to because we have the fourth, so this one has so Can you cancel and that's just going to give us route two And lastly we'll have Z which is going to equal Uh four times the co sign of the so that's for times route you over to and that ends up giving us to route to as our final answer

Our ultimate goal for this set of problems is to find an equation in spherical coordinates given the rectangular coordinates. So it's important to remember that um were given rectangular and we're trying to go to spherical. So what that tells us is that we have um Y equals two. That's it. That means x equals zero And z equals zero. So when it comes to finding row we know that rho squared is equal to x squared plus Y squared plus Z squared, but x squared, Z squared are equal to zero. So we really just have that row equals Okay, and that's going to be our problem to that. That's gonna be a result That we can consider other possibilities such as E equals six. If we end up getting something like z equals six then similar to what we had before, that's just going to end up telling us that row is equal to six because everything else is equal to zero, then we can consider other possibilities such as um expert. Plus y squared plus Z squared equals 49. We already know that again, rho squared is equal to x squared plus y squared plus Z squared. So row itself would be equal rho squared. We see as 49 That tells us that row is just equal to seven. Um These are all really good ways of showing this. We can also do other options um such as expert. Um Plus widespread equals 16. So we can combine other components knowing the X squared. Um since we know that X is row signed, the coastline data and why is roast sign the signed data? We can combine terms and end up getting our final answer.

So in the given question, I need to find a solution set for the given sort of equations. And I've labeled each of them as equations 12 and three. And now we proceed toe eliminate variables from each of these equations. So I start off with equations one and three and eliminate. Is it from them? So I just multiply one with three, and I just add one and three. And now I write the result in blue, which you'll give me six X plus nine y equals toe minus three. Now, I label this as equation four and now I just Yeah, proceed toe remove X from one and two. Now I multiply two with one someone to play total equation one and then just add it toe equation too. So this will give me Yeah, the next minus two X, which would be eight X and then six y plus ey, which would give me plus nine way on. The constant would be minus six plus three. Not when a sex it should be minus four plus three, which would give me minus one. And now I live with this as equation five. Now I proceed to remove the variable. Why? From four and five. So I just subtract for from five. Like so. And I get to access one. No. One. That should be too. So this would give me exiles one. Now I substitute access one in equation five, which would give me eight plus nine Y is equal to minus one. Now, this will give me what I asked. Minus one. Now I substitute both the values off X and Y in equation three. So this would give me one plus six multiplied by minus one plus said equals toe minus one. This would give me said us for mhm. And so the solution set would become one cower minus one and four.


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