5

Transform the given system into single equation of second-order x] = ~6x1 + Txz X2 = -Ix[ 6x2. Then find X1 and X2 that also satisfy the initial conditions (0) = 8 ...

Question

Transform the given system into single equation of second-order x] = ~6x1 + Txz X2 = -Ix[ 6x2. Then find X1 and X2 that also satisfy the initial conditions (0) = 8 Xz (0) = 9.

Transform the given system into single equation of second-order x] = ~6x1 + Txz X2 = -Ix[ 6x2. Then find X1 and X2 that also satisfy the initial conditions (0) = 8 Xz (0) = 9.



Answers

Solve the following system of nonlinear equations for $x, y$ and $z$ $$ \begin{aligned} x^{2}+y^{2}+z^{2} &=6 \\ x^{2}-y^{2}+2 z^{2} &=2 \\ 2 x^{2}+y^{2}-z^{2} &=3 \end{aligned} $$ [Hint: Begin by making the substitutions $X=x^{2}, Y=y^{2}$ $\left.Z=z^{2} .\right]$

Okay, So given these three system of equations, um, are there any I can automatically add or subtract to cancel variable? We'll have the same coefficient in front of wife for one and three. So if I subtract equation three from equation one, the wise will cancel. So eight minus 12 is negative. Four X negative three wide minus 93 by that cancels 16 minus. It's his native to Z equals negative two minus negative, too. Um, it's gonna be native two plus two, which is zero. So now I have one system of equations. Um, I want to cancel. Why? But I want to involve equation, too. So what I'm gonna do is animal supply equation one by three, um, and then added to equation three. So, equation, one times three is gonna be 24 x minus nine. Why? Plus 18 z equals negative six and then plus equation 3 12 x. Oh, sorry. That's equation to that. Should be there. So we're adding this to equation too, since we haven't used it yet. Four x plus nine wives plus for Z equals 18. When I combine those, I'll get 28 x wise cancel plus 22 z negative. Six plus 18 is gonna be 12. And then I know I can divide by two to each of these terms. It's They all have actress too, So this will be 14 x plus 11 z equals six. Okay, Now, what can I do to try to cancel? Um, anything I could also actually, no, that I'm looking at this. I could divide each quick each term by negative to to make this positive, actually, All just divided by pops it to keep that negative at each turn by two. This will be negative. Two X minus two minus Z equals zero. Divided by two is just still zero. And I want to try to cancel these, so I'm gonna try to cancel the thanks term. Somebody multiplied this equation by seven. Negative 14 x minus 14 a minus seven z and then 0 10 7. It's still zero. Rewrite this down here. 14 x plus 11 z equals six. When I add these together X's cancel, I'm gonna get, um, positive. Four z equals six and then divide by four to both terms. This is Zia's six of her four by two Z will be 1.5 or three over two. Okay, so now that I have Z, I could plug back into the green equation to try to solve for X. So negative two X minus 3/2 equals zero. Let's add three over to both sides. When I do that, this will cancel negative two X equals 3/2. And I'm gonna divide by negative to to both sides or multiply by one over negative one half same thing. So x will be multiple numerator and denominator. Negative. 3/4. Okay, Z, I have X and I want to find why I'm so I could put it into any of the originals. It does not matter which one. Someone A. Plug it into the first equation. So going back to the first equation This is eight times X of eight times negative 3/4, minus three y plus six times E, which is 3/2 equals negative too. Okay, eight times in a or 3/4 that Samos native 24 over four, which is negative. Six minus three. Why six times 1.5. That's standings 18 over to which is nine equals negative too. So combining, like terms and get three. Why, Um, plus three equals negative too. Subtract three from both sides. Negative Three. Why equals negative five. Divide by negative three. Why is five thirds? Okay, So then my final answer is gonna be one solution. X's negative. 3/4, five thirds and then positive three over to frizzy and all the equations above cross. Exactly the

Question Number 48. Here we inherited the augmented metrics for the given system of equation. Now, most of what we have to make one or here. Right. So for that, or appropriation is on one. Multiply by negative one tarred right. So we can make one over here. So he are faster. That is one your negative one told you had 24 divided by negative relieving, boarding. Negative. Right. And here, negative nine. Divided by a negative three, which is equal to three. And the second Royce as it is now we have to make zero. We're here. Or that our no patient is our toe minus two on one. Your four stories as it gives on the second row Bridges CEO, a tard Nate. And on the right side we have zero. Now we have to make a living here one. So we're operation is too. Multiply by tree by a again. Here are four stories as it is in the second release, Siegel one you are to buy eight multiply bait Read is equal to three and on the right said we have zero Now We have to make Syria where here or that Our prohibition is one plus one by tart times are so your second, Ruiz entities on the bus Troyes 10 negative seven. And on the right side, we have three Now. From the first row, we can write immigration. So your X minus seven that is equal to three. No subject X in this equation. So if you're exquisite gold two plus selling, then from the second row we can write any question that his wife must resent is sick or do zero subject Why? So you're wise equal to negative three said on that Is he called that. Which means that is or even your boat now, right? The gender solution Your ex is true Bliss seven Big. Why is it important to negative three set? And that is equal. Do that here is that it's any real member with Menchu's to see the general solution. Thank you

Were given three equations. Explosive, I said equals zero two x minus life plus the Equus minus one minus x less to me by my necessary equals to nine. Izzy you to find the video banks, whereas they're using groundless formula. So what does that say? That X is equals to determinant off x by day by Mexico's with no made up by by the surgical tree down wind offset by the we need to find the ritual people by the coefficients of X rays is what are the prohibitions? Want to minus 11 minus 1311 minus one. So we were stole the forming of the government, which will be used all over in this question that is a 11 in tow. Be due to see three to be toe three c 33 minus even to be a one. C 31 b 23 c 33 plus a 13 Determine indoor being one Steve 31 B two to unseat 32 This is the using. The ruling question now can clear the determined. So it is equal toe put in the values off a 11 even one. Is this two minus 131 minus one minus one in tow to minus 11 minus one. Last one in the to minus one. Minus one and three. So it is a for the word kalg lady the dominant. After where do my tricks Cross will deploy the values and subtracts the one in two minus one in minus one minus Well into three miners, one in tow to in tow minus one minus one into minus one plus one into movinto three minus one into my list. So it is equal to work. One into one, minus three, minus one into minus two. Bless one. Thus went into six minus one, which is equal to minus two bliss. One mess. Quite it. Is he gonna do four? No, we have these equals two. For now, we will find Theo Fix. But that in the we will replace the ex school visions Wendy Constants or the question So that is what zero minus one and minus a gaping hole Metrics as it so that is one minus one 311 minus. So what will be the Formula? A zero into minus 131 minus one, minus one Into minus one minus 81 minus one plus one into minus one minus eight minus one. And so it is equal to work. Scalpel. It will put zero will remove this one because anything multiply by 00 will move for the minus one into minus one in minus one minus one in do minus eight. Then plus one into minus one into three minus minus one into minus beat. So it is equal to minus one into one. Plus eight plus one into minus three. My equals minus nine. Minus 11. Because it was too minus two. It not similarly for the way we will replace the coefficients off. Bye bye d efficient ones or the way we will replace the coefficients off by with the constants of the equations. What? Becomes one to minus 10 minus one minus 81 gun and minus one toe. Water to the Terminator one minus one minus 81 minus one minus zero in two to minus one. Bond minus one plus one in two to minus one. Minus one and minus eight. So it is equal. It is. It will the work one into minus one into minus one minus one in minus eight. We will not write the second expression because you know, multiple of anything will be zero. Let's move further. It is blessed one into do Indo minus it minus minus one in minus one. So it is equalled. Would one in the one less a. This one improved minus 16 minus one, which is equal to nine minus 70 which is equal to minus Swigert the devious minus C Now we go. Ladies it Now what will do here is will keep the values or proficient off the x and y as it is on replacing coefficients observed by the consent of the questions with This is a magic with this one. Now we gotta let her so one into minus 13 minus one minus eight minus one into two, minus one minus one minus said was zero into two minus one minus 13 So it is equal to one into minus one in minus. Dead minus minus one into three, minus one into tool Indo minus aid minus minus one in two minus one. Your expression we will not right, because anything but the papal busier over a zero. So 18 plus three minus one in tow, minus 16 minus one, but is equal to 11 plus 17 liquids to renting it. What is so they've what is X access? The off X, which was minus two indeed. Divided by David is four. It is equal toe blindness fight. What is why? Why is the York by witches minus eight. Very burdened by TV. Just forwarded. Comes out to B minus two. Then what is it is there is equal to the O. Z. But a model 24 by David is school. It is equal to sit. So therefore, solution is minus bi minus two months. It

Okay, this question asked us to solve a system of nonlinear equations. This time we have X squared, Y squared Z squared. Um And as with previous exercises, it gives us this hint that we should make that substitution. Um Where like a bigger X I guess is equal to X squared and why bigger Y little Y squared, capital Z is equal to Z squared. So that allows us to just take the coefficients like we normally do and put them into a matrix. So that's what I did in black here. Um This first matrix is just taking the coefficients, putting them into the matrix after making that substitution. Um So we're trying to solve this. So we want robert is echelon form um things to notice right off the bat is that I already have this leading one in that first position. That's what I want. Um So that's really nice. What I want after that is to go back and make substitution. Is using that in order to make both of these slots. The one and the two here be zeros. So that's where I'm going to start with. Um My row operations, I'm doing negative one times row one and then adding to row two and negative two times 01 adding to row three in order to make um these lots P. Zeros. So we see that that's the case um wrote to and we're three. All of that changes, not just that first slot but um that's the reason why I'm making that move then let me stay here to that. Um Your row operations might not look the same as mine and that's okay because there's lots of different ways to about this. Um But this kind of gives you a systematic approach I think. So um My next um goal I guess with this is to make this lot be a leading one as well in that y column. Um What I noticed though is that like on this bottom row, I almost have a one, like I have a negative one there and so it would be easy for me to just move that up and change the signs. So that's what I chose to do here, you can go about this differently like I said. Um but I switched through two and three, so just from here switching those rows um and then I went ahead and changed all the signs that were in row three now grow too. So we have the 013 and 902 So um where we've gotten to is leading ones and rows one and two. Now we can go back and make a substitution in order to make this negative two is zero. So that's my next step. I did that and notice here We have that triangle of Zeros that we're always looking for when we're reducing. So we're in a good spot so far. Um leading one leading one. I want this to be a leading one as well, so seven and 14 both divisible by seven. I'm choosing to multiply that bottom road by 1/7. Um and then I'm going to go ahead and do substitution zall in this stuff because um hopefully you can see that wouldn't be too bad. Um I want, oops, I want this three to be a zero, I want this one to be a zero. Um so those are the other two steps that are kind of taking place all at once here. So um we got two leading one in this bottom row. We took care of these zeros here and here. I want this to be a zero as well so that it's completely in row reduce national in form. So that is our last step to take um negative one times row two and add it to grow one in order to get that last one out of the way. So um this is our final row reduce echelon form of the matrix. So this red matrix is what we're working with to about solving this for X, Y and Z. We have to take into account that we have made some substitution. So we said that um X was equal to X squared between this is a capital X. Um and so we know that X is equal to one, so that means that X squared is equal to one. Um So for that to be the case square both sides. If you want X has to be equal to positive or -1. Um Next we know that capital Y was equal to y squared, so Capital Y based on the second column, second row. Um so I can call them being wise, I mean go ahead and label those. Um from the middle row, we know that why is equal to three? So that gives us that. Why squared? Little y squared is equal to three And so Y is equal to plus or minus the square root of three. And lastly we know that big Z is equal to little Z squared. Big Z was equal to two based on the matrix. And so Z squared has to be equal to two. So little Z is equal to plus or minus square to to. So these are final answers are the pieces of our final answers. Final answer that X is equal to plus or minus one. Why is it little plus or minus square two? Three NZ is plus or minus square root of two.


Similar Solved Questions

5 answers
Suppose F(t) has the derivative f(t) shown below,and F(O) 4.Find values for F(1) and F(7)F(1)PreviewF(7) Prcvicw Enter your answer a5 & number (like 5,.3,2.2172) or as a calculation (like 573, 2*3, 5+4) Enter DNE for Does Not Existy 00 for Infinity Get help: VideoPoints possible: This is attempt of 3. Message instructor about this question
Suppose F(t) has the derivative f(t) shown below,and F(O) 4.Find values for F(1) and F(7) F(1) Preview F(7) Prcvicw Enter your answer a5 & number (like 5,.3,2.2172) or as a calculation (like 573, 2*3, 5+4) Enter DNE for Does Not Existy 00 for Infinity Get help: Video Points possible: This is att...
5 answers
Mananoinec quesuon will eave ttws [ pontseuastion 157f tcn Uic > talk otrut #atiutk (ptcobyFoundAif thc populalicn mecnsample of 800 mcmbcrs 14,5135 Nonc of thesc17,71760,05notner questionniste,pon.MovingToekibey
Man anoinec quesuon will eave ttws [ pontse uastion 15 7f tcn Uic > talk otrut #atiutk (ptcoby Found A if thc populalicn mecn sample of 800 mcmbcrs 14,5135 Nonc of thesc 17,7176 0,05 notner question niste,pon. Moving Toekibey...
5 answers
Part CWhat is the major product of the following reaction? CH; CH;C=CHz HSOs H,oDraw the molecule on the canvas by choosing buttons from the Tools (for bonds); Atoms, and Advanced TempHt p0 0 0M ; G ;2Marvin JSChemyonSubmitRequest Answer
Part C What is the major product of the following reaction? CH; CH;C=CHz HSOs H,o Draw the molecule on the canvas by choosing buttons from the Tools (for bonds); Atoms, and Advanced Temp Ht p0 0 0 M ; G ; 2 Marvin JS Chemyon Submit Request Answer...
5 answers
Mi:tr SealtmBackHW: Momentum pdfTulakcudDueeennlarun 44 4 4 M_4Fhi4mit u#L EetD TAHETTATT#Ean IFLIETa4n (Lck 4 dAnneEEDFmna Iritu 2cnun LEcntnte #etnn DaCETAc Ihl Eia HiL [email protected] EiZtzZ Teki ImFFIan FettDotal Cupr 536 EllE ( ZZ= Yanuke und Guectke yntan Kie Iuduz Itul tclactnlbeaDE[nFibT ] =9#Eacu] uula RAAEFEu Annent ete 2 7 Pen KttPreviousNextpashooardCalandarKotincationsHndor
Mi:tr Sealtm Back HW: Momentum pdf TulakcudDueeennlarun 44 4 4 M_4Fhi4mit u#L EetD TAHETTATT #Ean IFLIETa4n (Lck 4 dAnneEED Fmna Iritu 2cn un LEcntnte #etnn Da CETAc Ihl Eia HiL [email protected] EiZtzZ Teki ImF FIan Fett Dotal Cupr 536 EllE ( ZZ= Yanuke und Guectke y ntan Kie Iuduz Itul tclactn lbeaDE [nFibT ] ...
5 answers
5. !) How many grams IS 5.28xidsmolacules c FlucaneHA Fluorioe 19.00 glmal2S 5.28 >10 mlus mol F 19.003 F [6.022*10 molcults ( Mal ?bb5.89/73 9 F =|.67x /0 3 9 F Ccn' Gad my Grrr Pleasc Help-
5. !) How many grams IS 5.28xidsmolacules c Flucane HA Fluorioe 19.00 glmal 2S 5.28 >10 mlus mol F 19.003 F [6.022*10 molcults ( Mal ? bb5.89/73 9 F =|.67x /0 3 9 F Ccn' Gad my Grrr Pleasc Help-...
5 answers
Assuming that 4 in 10 automobile accidents are due mainly to a speed violation; find the probability that among 10 automobile accidents , 6 will be due mainly to a speed violation0 a 0.009b 0.93080.7520D0.1114t0.0.2090
Assuming that 4 in 10 automobile accidents are due mainly to a speed violation; find the probability that among 10 automobile accidents , 6 will be due mainly to a speed violation 0 a 0.009 b 0.9308 0.7520 D0.1114 t0.0.2090...
5 answers
A group of students are t0 conligure 3 capaeitors as shown in the circuit below_ to obtain the maxium equivalent total eapacitance between points _ A and B Determine the value of C Ma and assign values below to the capacitors C, Cz, and C,,to obtain this value (Cmux). 2.50 AF, 3.2 AF,5.5 HF
A group of students are t0 conligure 3 capaeitors as shown in the circuit below_ to obtain the maxium equivalent total eapacitance between points _ A and B Determine the value of C Ma and assign values below to the capacitors C, Cz, and C,,to obtain this value (Cmux). 2.50 AF, 3.2 AF,5.5 HF...
5 answers
V com filrtakeAssignment/takeCoval 3 statement both 1 1 Rcfee lentActivity do?locator products gteeotn is true or fake for the transfomnation pictured at the particulale 1 assignment 1 1 -take level Tollontg
V com filrtakeAssignment/takeCoval 3 statement both 1 1 Rcfee lentActivity do?locator products gteeotn is true or fake for the transfomnation pictured at the particulale 1 assignment 1 1 -take level Tollontg...
5 answers
(1 point) Find y as a function of t if36y" 60y' + 25y = 0,y(2) = 2, y' (2) = 2 y =
(1 point) Find y as a function of t if 36y" 60y' + 25y = 0, y(2) = 2, y' (2) = 2 y =...
5 answers
An equation of a parabola is given. (a) Find the focus, directrix, and focal diameter of the parabola. (b) Sketch a graph of the parabola and its directrix.$$5 y=x^{2}$$
An equation of a parabola is given. (a) Find the focus, directrix, and focal diameter of the parabola. (b) Sketch a graph of the parabola and its directrix. $$5 y=x^{2}$$...
5 answers
Suppose for some transformation T, MB (T) 55 where 9 is the standard basis. Which matrix represents MS' (T) when 2' {(-1,3), (2,4)}? 52 A. 8 1 B. (-5 -8 C. 1 _ D (3 C1
Suppose for some transformation T, MB (T) 55 where 9 is the standard basis. Which matrix represents MS' (T) when 2' {(-1,3), (2,4)}? 52 A. 8 1 B. (-5 -8 C. 1 _ D (3 C1...
5 answers
Thcre = MFCtD internet COmpanics BytosA-Loss luudl 839 million dollnns of sks in 2012 ak| sks wcm iwerensing hy S3.1 million dollars pCr 'ar ; Net Outlet hud $46.2 million dollans & sakcs in 2012, And salcs "ere increasing by SL9 million dollars per Jear: In what year will the companics have the same sales?
Thcre = MFCtD internet COmpanics BytosA-Loss luudl 839 million dollnns of sks in 2012 ak| sks wcm iwerensing hy S3.1 million dollars pCr 'ar ; Net Outlet hud $46.2 million dollans & sakcs in 2012, And salcs "ere increasing by SL9 million dollars per Jear: In what year will the compani...
5 answers
Let A (Zp[r]) f(z). Here, p is prime and f € Zplr] has degree n. Then class of €.Zpla], where a is thef(a) = 0 in A and no smaller polynomial kills a. That is, if deg(g) n then g(a) = 0_ (b) A has exactly p" elements_ (c) A is a field f(z) is prime in Zplz]: In that case, then Bp" B for every B € A.
Let A (Zp[r]) f(z). Here, p is prime and f € Zplr] has degree n. Then class of €. Zpla], where a is the f(a) = 0 in A and no smaller polynomial kills a. That is, if deg(g) n then g(a) = 0_ (b) A has exactly p" elements_ (c) A is a field f(z) is prime in Zplz]: In that case, then Bp&...

-- 0.078158--