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P680.2h,0P680Ps80P680-mtP680*=t P68o -Ps80P680*~N...

Question

P680.2h,0P680Ps80P680-mtP680*=t P68o -Ps80P680*~N

P680. 2h,0 P680 Ps80 P680- mt P680*= t P68o - Ps80 P680* ~N



Answers

$\mathbf{X}(t)=\left[ \begin{array}{ccc}{e^{t}} & {e^{-t}} & {e^{2 t}} \\ {e^{t}} & {-e^{-t}} & {2 e^{2 t}} \\ {e^{t}} & {e^{-t}} & {4 e^{2 t}}\end{array}\right]$

In this problem we are going to use the properties of mattresses and they're in verses in order to simplify a given mattress expression. Now the given matrix expression is E C inverse whole inverse times E C inverse times E C inverse whole inverse times E. The envious Now in the question it is said that a B C and D. Are all in vertebral mattresses. Now let us begin to simplify this expression. Now, first of all, what we have is easy inverse inverse times, easy inverse. That means that the matrix easy inverse has its inverse multiplied with this original matrix. Now, since the product of any metrics with its inverse is equals identity matrix. Hence a C inverse inverse times a C. In verse will be the identity matrix. I. With this we multiply the remaining two terms A C inverse inverse times a. D. In verse. Since any matrix multiplied with the identity matrix, is that mattress itself? This will be equals to A C. Involves inverse times A. D. In Vegas. Now using the property of matrix inverse, which says that a B hole in verses equals to be inverse. The inverse E C inverse hole in verse will be equals to see inverse inverse times a inverse. And with this we multiply a. D. Universe which are the last two terms of that expression. Now see inverse inverse will be equals to see because the inverse of any inverse is the original matrix itself. Next we have inverse. E be endless. Now, since matrix multiplication is associating, we can group together the terms however we want without changing the order. So let us group together to terms a university. And then we use the property that the product of any matrix inverse is equal to the identity matrix. So inverse A. Will be equal to I. And we are left with C I. D. In most now since the product of any matrix of the identity matrix is the matrix itself and ci is equals to see. And with that we have at the end the in laws, so that means that our metrics expression is simplified to CB in Vals.

Question is which of the following is not a crime try and receive is represented by that molecules that have actually get so we can observe that he'll start strong feeling and so it will be good to have and industrial. So first option is BDCL four who minus. So it will be, it always Bs people have palladium and platinum is always so people have read so correct on duty.

In this video, we're gonna go through the solution. Thio question first to chapter 5.4. We asked to find just the form off the particular solution to the following different equation. You know, I still actually find what the secret solution is. Well, they're just full of it. So first we look at the genius part and it would help if we write this in a slightly different way by taking out a factor off e to the two tea that leaves us with one last ti course. See square. So now we have a on exponential part on a polynomial part, as that motivates a form, uh, follows. So we want a an exponential part with and to t because we already have the bot in the in her in her genie genius term. And we want a general second order polynomial. So a one cause eight Sorry. 88 0 was a one Time T plus hey to times t squared. There's nobody going any higher order in porno Meo because all those trophies zero and one final thing we need to track is the roots of the auxiliary equation. Because if the roots, if it is a room off, too. And that will mean that we need to change the form somewhat. So the exhibit equation is R squared minus one equal to zero, which has solutions are equals plus a minus war, neither of which are equal to two. So therefore we're happy with this form for ah particular.

K two Cr awful gives a yellow precipitated it's a yellow policy heated on reaction with on reaction with Be a two plus, as well as B B two plus, therefore, option C and option the uh, correct answer for this problem, Option C and option B. R. Correct answer for this problem.


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