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#ot roknrix blow Su Pmse is ~rodnx Forr 0 stslern 4& Audmen-ed QF A;reon @ 9xaclions % +~ ~] L? ad does #e Foj7 Wld vauueb) sys err have 0 uriane soluhon 6) irh...

Question

#ot roknrix blow Su Pmse is ~rodnx Forr 0 stslern 4& Audmen-ed QF A;reon @ 9xaclions % +~ ~] L? ad does #e Foj7 Wld vauueb) sys err have 0 uriane soluhon 6) irhrily rraeny salchms No sol_ xior

#ot roknrix blow Su Pmse is ~rodnx Forr 0 stslern 4& Audmen-ed QF A;reon @ 9xaclions % +~ ~] L? ad does #e Foj7 Wld vauueb) sys err have 0 uriane soluhon 6) irhrily rraeny salchms No sol_ xior



Answers

licre the ycllow and orangc precipirares arc, rcspectively (a) $\mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{2}, \mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{-}$ (b) $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}, \mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{2}$ (c) $\mathrm{Na}_{2} \mathrm{CrO}_{4}, \mathrm{~K}_{2} \mathrm{CrO}_{4}$ (d) $\mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{2}, \mathrm{~K}_{2} \mathrm{CrO}_{4}$

So in this problem we're given this matrix which Is a diagonal, right, only has entries on the main diagonal. Everything else is zero and were asked to define the determinant. We can use a matrix calculator to do this with. So what you desmond dot com went to math tools matrix calculator and got this one. So I need a new matrix now and I got five rows and five columns. And the first entry up here Is a -2 And then the entry here is a three And the entry here is a -1 man. She just working my way down the main diagonal here, This is a two And the last entry down here is a -4. There's all my entries now to do the determinant. I go d E t of a and We get -48 for the answer. So there you go. Which by the way, if you multiply the entries on the diagonal there. Look what happens When one is 2 times three is -6. I was in -1 is plus six times two is 12 Times of -4 is -48. Gave us the determinant, didn't it?

Hello. The potion is taken from differential equation and we have to solve this first order differential equation. So let me initially variety exponential to the power X. The ancient of why the eggs plus one minus exponential X. Second square while. And then the way is equal to zero. Taking the X. Part of the situation to the left hand side. And why part of the right hand side we get exponential. The X divided by one minus exponential X. That is equal to oh minus second square Y. The Y divided by being gentle by. Okay now let us integrating both sides. Let us you do the integration on both sides. So that equation becomes in order to integrate it let one minus E. To the power excessive 40 T. We get minus E. To the power X. Dx is equal to did you taking negatives and also to the items I tweeted negative sign here. Okay. And it's a similar way let the ancient Y. Is equal to that. So we get a second square Y. Dy is equal to the let me substitute these values in the equation. So we get integration -80 over T. Which is equal to minus integration. These it over that. So if we saw we get the value minus you know Wolf G. Is equal to minus lobo said plus you see the monster and organization just canceling the negative sign on both side. We get low. Wolf T. Is equal to novel said plus see when there's a new bone strange or integration T. Is equal to we remember that is one minus E. To the coverage and that is equal to low. That is I think that is tangent of life. Soon it will be being gentle. Why? Okay let's see by taking this storm to the left hand side. We get logo one minus E. To the power X minus logo. The gentle play. It's equal to see by by using the formula logo A minus logo B. Is equal to local. A baby indication. We get no one minus E. To the power X. Divided by the in gentle. Why is equal to see applying Okay taking a look to the right inside we get one minus U. To the power example. Indian to why is equal to exponential to the power supply. So from here we get a new constant of integration. We get one minus U. To the power extrovert engine. Why is it well too A is a newborn strand of integration which is the required solution of the aggression. All this clears your out and thank you

Okay. Good day, ladies and gentlemen, today we're looking at problem number 23 year, which involves so lovingly and sugar all your problems number 23 and as normal. So the first birthing we observed is that this is a linear second order, ordinary, different show equation, homogeneous and with constant coefficients. So we just plug away using the technique we developed so far. First begins the auxiliary equation, and in this case, is just r squared minus four are close to ah, And then once we get that, we just look at the roots of the auxiliary equation. And in this case, we see right off that that we have to just sting riel roots eso with that information. Then we can just go find the general form of the solution. Which, of course, has this form. You'll notice that I started used the instead of plugging in the actual values for our who. Uh, these this point of sort of saved my whole little, um just by writing are one and are too furthermore, um, what you don't ever want to do, at least in a mass courses, right? Try to right. Square root too, is something like one point or one or something like that. Never. Never do that. Always. Always, always, always, unless you're directed. Otherwise, you're right square root to or you go, you know, square root to or whatever. But you never use 1.41 or whatever something like, uh, never do that. A mass course. I was used to close form. I've seen that a number of times, and I tell you, it's and mouth courses. You always use the form. You know, there's a reason we have the square root sign. And you use that for me, even if the number of his ends up in your rational. Um, okay, so the next step system so off the industrial value problem. And to do that first used the initial conditions to set up the system of linear equations. Um, pretty straightforward where I got these guys from, uh and then what? This The next step, of course, is to solve it. And the way I do it is, um I use that the augmented matrix form. So I love for this kind of stuff. I think it's the best way to do it. Um, and then just using matrix operations. I get, um, this guy here, over here. Sorry, but, uh, come close. But I end up with this using just matrix operations. Of course. Um and this, of course, tells me that I get the solution for the end. For the, um, sorry for the, um, initial value problem in this form. Uh, just this is my C one, of course. And this is my seat, too. Ah, and that simple thighs. Just using the cortical magic, if you will, of algebra, um, to this here. And that is our correct answer. And why I just simplified it with the one over two square two and two into this guy because that was the form of the answer given, um, in the in the in the answer there. Okay, so that's it for this problem again. If there's anything that you're unsure of here, um, if any of the steps you don't understand, um, just go back and shock and look at earlier, um, venues on the, um which Michael on these These forms off ordinary differential equations. They're straightforward equations. And you really should know what those terms means. No. When he said he had constant coefficients it was second order linear so on and so forth. These terms means something, and they give you a lot of information about solutions on how to solve it. So knowing what these things mean to be can be very healthful. Uh, in the long run. Okay. So thank you very much for your time.

In this video, we're gonna go through the answer to question number 35 from chapter 9.3. So it has to show that the Vector X, which the function of tea is a solution or rather satisfies at the system the differential equation system given here. So, first off, we wanted to find the derivative of thanks its function of tea, So just do this. Each of the elements. So that was over. The top element is three e to the three. T. The bottom element is two times three, just six, eight and three t. Okay, Now let's find what the right hand side is. So that's one one minus two for times by X. As a function of tea, this is gonna be the matrix 11 minus two, four times by eater three t two you to the three to. So this is gonna pay each of the three T plus two eaten three T, which is three e to the three t in the time element on the bottom element is gonna be minus two eaten sweetie plus eight, which forced us to a three d so minus two plus eight is plus six Hey, so the three t which is exactly what we found when we took the derivative off X has dignity. So yes, the vector were given to satisfy


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