is-the-following-difference-equation-of-order-3-explain-y_k35-y_k26-y_k10

Name: is the following difference equation of order 3 explain y_k35 y_k26 y_k10
Uploaded: 2019-09-01
Duration: 2 min 54 s
Channel: Numerade
Description: Is the following difference equation of order 3$?$ Explain. $y_{k+3}+5 y_{k+2}+6 y_{k+1}=0$

Question

Is the following difference equation of order 3$?$ Explain. $y_{k+3}+5 y_{k+2}+6 y_{k+1}=0$

Nikolaos Alexandrakis · Accepted Answer

way. Want to look? Find the order off this discreet regulation. Now, as we know from theory, the order off the discredit creation is the difference off the highest you dicks to the lowest index. But any three is here is a perimeter. So if it is no zero, then we immediately have that. The order is three, cause we have K plus three minus G sequence three. Now, if a three they&#x27;re called zero Oh, just to fix this three, then we proceed with a difference off. You&#x27;re a blustery and your plus one. And the difference is too if a two is not zero because okay, plus reminders. Okay, less one that close. Go now if a door he&#x27;s zero. Then again, the difference with the order of vacation will be the difference Off the fire started their toe toe the next. So the first Norman reveal or their, uh their toe to the order off the third off the first non trivial term. Then if a one is not zero, then the corresponding or there is one. Otherwise, we have the correspondent thing or there is zero minutes. Otherwise, we have why gay plus three queens zero with which would later toe like a a quint zero, which is review

Michael Jacobsen · Answer

in this example, we have 1/4 order difference equation that&#x27;s provided here, and our goal is to do the following. So our goal is to write this particular equation in the form of a vector. X K plus one equals a particular matrix, a times except K. So if we can determine what the Matrix A should be and what the vector except cave must be, then our work is complete. Let&#x27;s do some early analysis on this. This particular equation is a Order four difference equation. That means our vector X K is going to have four elements all together. Next, let&#x27;s use a theorem that&#x27;s also going to guide our work. So the theory tells us if we have a difference equation of order N, then we&#x27;ll have a vector x k that&#x27;s formed in this way with four entries altogether, we start with y que then increase on the sub scripts on K. So the second entry is why K plus one. Then why K plus two? Finally, why K plus three. Now we&#x27;re ready to describe the Matrix, and if we have a order, N and N is equal to four r matrix is going to be of size four by four. Let&#x27;s make it appropriate size for that task. And what the rose air telling us in this theorem is will start with a zero will produce a one and then the remaining entries are all zeros. So I have 0100 as the first row of this matrix. Now, the theory tells us that the only difference amongst the Rose is that if there was a pivot here, the prove, it moves down to the next column and then we&#x27;ll have zeros thereafter. So back to a matrix say will go 00 place or pivot here and places zero next. Next, go 000 and place the pivot here. And that&#x27;s our 1st 3 rows. Now the next key part are these quantities that we see here in the final row. Notice the sub scripting the sub scripting tells us that will have in our case and a one to be negative. Nine. A two is six. A three is eight and a four is equal to six. So oh dear, rather than the sub scripting before our A one is negative. Six. A two is eight 83 6 and a four is negative nine. So don&#x27;t make that mistake. The sub scripting increases from left to right, starting with E K plus three for the Order four Difference Equation. Then we go in the reverse order, starting with a four. Take its opposite. So we need the opposite of this quantity, which makes it a positive nine produced here. Then the very next one. We take the opposite of this value, so we&#x27;ll have a negative six. Likewise, take the negative off A two for a negative eight. The negative off a one gives us a positive six. And now we have produced the required matrix. So with this matrix given here with XK provided here, we now have this particular equation which captures the same information as the original difference equation.

Nikolaos Alexandrakis · Answer

we will right this third or their difference occasion as the first or the system in the form X killed plus one. We will write it with over line just to know that this is a vector. It was a times ex gay Which way is three is three times three mavericks Since we&#x27;ll have the thunder, their system and we proceed by considering the vector x t Uh, it&#x27;s consistent these three values and the vector x k plus one which is this vector for following the definition off ex gay and we write Get with the foot taking the talk on the information from thing this and get some of them got played Tow the federal court in areas see off Gabe Plus three equals three over four CK plus two minus one over 16 ck and we perceive as in the book. And, uh, that&#x27;s an example of the book. And we write it as they seduce them in the for month eight times ck where a equals one or one 01 and minus one over. So extreme. Oh, and city over four. All of these times, the vector X Games

Smita Praharaj · Answer

okay. In this question, we asked to determine the order of the differential equation by Prime plus y equals +23 y Square. It&#x27;s recall that the border of differential equation is the highest order, derivative and equation. Now, how do we determine what stuff under order? Derivative. So if we have the derivative y prime, that&#x27;s the first derivative. So it has ordered. What if we have? Why Double Brian? That&#x27;s the second derivative. So it has ordered to, Similarly, by Triple Prime has ordered three and so on. In this equation, we have only one derivative, which is why prime, so the order equals toe.

Grace Muhihu · Answer

Okay, So to subtract thes two are gonna first distribute the negative. That&#x27;s between them. So that&#x27;ll have 56 Why cubed plus 1/2. Why? Plus three. And then now when I distribute the negative, I&#x27;ll have +16 Why cute minus y squared plus three wide. It&#x27;s enough. I just add and combined my life terms will have 56 y cubed +16 like you. That just gives me why cute. And then here I only have one y squared term. So that&#x27;s gonna be minus Why square And then I have two terms here with y So I have 1/2 y plus three y not gives me plus seven halfs. Why and then, lastly have only one constant here, just just three. So I could tied about right on. So my answer here is gonna be y cubed minus y squared, plus seven halfs Y plus three

Problem

What is the order of the following difference equ…

Problem 31 Easy Difficulty

Is the following difference equation of order 3$?$ Explain. $y_{k+3}+5 y_{k+2}+6 y_{k+1}=0$

Answer

2

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

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Caleb E.

Kristen K.

Vectors Intro

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Linear Algebra and Its Applications

Lily A.

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Vectors Intro

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David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Lily A.

Anna Marie V.

Caleb E.

Kristen K.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications