5

0 A: Cx ~ dedydx...

Question

0 A: Cx ~ dedydx

0 A: Cx ~ dedydx



Answers

$\mathbf{A}=\left[ \begin{array}{rl}{0} & {1} \\ {-1} & {0}\end{array}\right]$

We won't get the fundamental methods of the system. Exodus shifty equals the metrics. Aim, multiply. But it's 50. First we get the Eigen values and the anger Victor's or the metrics in we have the metrics in is you, is you you zero minus one zero one zero. We subtract our from the Dagnall we subtract are from level with these metrics and the queen this new metrics to zero. By solving this equation, we get the Eigen values off. The metrics eat. They have minus are not employed by the small metrics minus are minus one one minus are plus one But tabloid boy a small metrics is small metrics One month tabloid boy, small metrics zero minus are 01 and this equals you. Then we have minus are but the boy boy minus R minus. Our units are multiplied moments r equals R squared minus minus one because plus one, this one multiplied by zero equals zero. This old equals 20 This means we have r equals zero or r equals most of or minus I. We have three routes of or four the report. We can get the Eigen vector corresponding to the rebirth by putting r equals zero by putting the r equals zero. In the former metrics, you get the same metrics a zoo 01 zero zero minus one 01 zero. But the boys by the wagon Victor, you want you to you three. And this multiplication it calls you from the first equation off this multiplication we get that u three equals zero from the second multiplication. From the second a question we get that also, boy three u three equals you. And from the third question we get that we get that you to equals you. This means that we have you two equals zero and you three core zero, and we can put you one with any value we can put you want. As usual, we put it one. Now we have the again Victor, corresponding to the real Eigen. Value U equals one zero and zero. Then we move on to calculate the again Victor off the complex, bark off the complex Eigen values here. And we should remember that we have over equals zero and we have later equals one. Now we can Could it for r equals, for example. Oh, we get the metrics minus Oy there. One zero minus Ali minus 101 minus oy. But deployed by Haiyan. Victor said one toe and the three equals zoo. By putting that one equals one, we can get from the first equation off this multiplication that minus oy. Plus that the three equals zero. Which means that the three equals I. And from the second equation, we get minus are multiplied by two minus that the three which is now oy equals zero. This means that we have the two equals minus one. The two equals minus one. Then we have the Eigen vector corresponding toe. The comics again values one minus one. And I began as usual. Great real board and complex sport one minus 10 plus 00 and one. But the boy boy. This means we have here and be we have all for better and be Then we can continue to get the three solution. Oh, our problem, x one of t. It was C one, my tabloid boy e to the about off all 40. It was about a party because this is a real birth multiplied by you. We have C one. It was about our key we have are zero and we have you. I remember that we have you 10 and zero. The second solution next to equals C two with the boy Boy e was about Al Fatih. We have all four equals zero multiplied by cosigned beta team. We have better one then cause I ain t deployed by the victor A. We have a one minus one and zero. We have a from a previous step year on year minus. It was a lot of already deserves you. So I in vicinity well supplied by the Victor B which is 0011 We can get exit three by switching designs and science and the negative sign meeting between Lloyd by C three multiplied money. It's about poverty. Slain t multiplied by the victor A. It was about 40 cause I in 30. But the blow by the victor v there we can get the fundamental ethics which is the final solution by getting the victors. Besides C one C two ancestry we have here 10 Do we have here that in between the brackets and here also the third victor off the Internet and metrics. Now we can get on the Newton metrics. X off key equals the first victor we have. It was a worldview is one 10 and zero. The second victor comes from X to we have cause I NT minus clanky and most of scientific or minus scientist E because we have here negatively. And the third Fichter comes from Exit three. We have Scient e Mina sci fi and cause I in team, and this is the final answer off our problem.

This video, we're gonna go for the answer to question number 29 from chapter nine point. So we have to find the values of our for which the turbulent off a minus our eyes equal to zero where he was given by this by three Matrix. What? Okay, professor, we want to find Ah, yeah, the servant off any minus I So you gonna have are in the top left. Zero they were. We have zero, then one minus are in the middle. A easy at the element of a is one and zero and one zero one minus. Huh? The seven of that is gonna be well, evaluation it along. The top row going are tied by the bomb. Right hand at seven in the bottom. Right. Hunty biting matrix. Which is what minus r 001 minus R. This is just gonna be easy. Calculated is ah times well minus r squared. We're looking for the values of off which that is equal to zero, which are clearly just the values, uh, is equal to zero. Ah, What

In this motion we have to use the reduction to find the universes of the given mattresses if they exist. And check it by multiplication. Let us consider the metrics deal one 10. And on the right side identity metrics or for that too 10 01. Now we will roll reduce the parliamentary. They will interchange. Okay. 1st and 2nd role our metrics becomes talk 10 01. And on the right side. Do you know? one 10. So we can write a universe equals two 0110. Now we will check it by multiplication. We will multiply a matrix by invest matrix. So we can write 0110 multiplied by 01 10. Now we will do the multiplication. Mhm zero times 0. We will first multiply first row with first column zero times zero plus one times one. Now we will multiply first love this second column. There are times one Plus one times 0. Similarly, we can write one times zero. The first few times one one times one Plus zero times 0 own simply find it began to metrics 1001. So we can t inverse matrix Sequels to identity matrix. Mhm. Thank you

Okay, so here we have he second derivative of why is equal to Why so make the substitution. And that V is equal to the first president of why. And that means that when we take the derivative of V will get the second derivative of why which of course, were given in this equation. So that's gonna be equal toe. Why? So this is essentially the system we're using, Right? We have B is equal, the white prime and that be prime is equal toe. Why? So this means that DVD t r do the B is ableto why and d y d t here, if you read from right to left, is equal to V so then we'll do the standard thing where we take, um morning divided by the others We get d v d Y is equal to why over v Okay, this is separable. So we get V. D. V is equal to Why de y If we integrate both sides, we get one half d squared is equal to one half. Why squared Plus to see See being some sort of constant eso This this v squared one half b squared minus one half y squared be equal to a constant is a standard form for a hyper Melissa, You can expect, uh, to see director. Is that have that curvature to them? Now, you can see that when we are solving for critical points and we want to set thes equal to zero. Um, we would just get y equals zero v equals their rights. So are 00 on the B Y. Accesses are critical point. So when we want Thio schedule, autograph it. So we let 00 be a critical point there, and we'll find trajectories that look something like this. Okay, so approaches the point and then kind of falls away from it. Okay, so that's gonna be a saddle point.


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