5

Find valuestor which the equationhas only ono "soiulon2kr + (-2)k-(-16) =Ancwor:Writo your list ol distinct = walobatwoon equaro brackotscopatuled DN commas; 0...

Question

Find valuestor which the equationhas only ono "soiulon2kr + (-2)k-(-16) =Ancwor:Writo your list ol distinct = walobatwoon equaro brackotscopatuled DN commas; 0 0 [-2,4,71,

Find values tor which the equation has only ono "soiulon 2kr + (-2)k-(-16) = Ancwor: Writo your list ol distinct = walo batwoon equaro brackots copatuled DN commas; 0 0 [-2,4,71,



Answers

(Print distinct numbers) Write a program that reads in numbers separated by a space in one line and displays distinct numbers (i.e., if a number appears multiple times, it is displayed only once). (Hint: Read all the numbers and store them in list1. Create a new list list2. Add a number in list1 to list2. If the number is already in the list, ignore it.) Here is the sample run of the program: Enter ten numbers: The distinct numbers are: 1 2 3 6 4 5

Hi, everyone. So that question we're looking at today gives us these 23 by three major cities will call and be, um and we need to use Jordan canonical forms to determine whether these air similar to each other. So remember that similarity. So let's say a is similar to be that means a equals s inverse times B times s for some in vertebral matrix s. And the way we use Jordan canonical forms is by saying, Well, um, I have two things are similar to the same matrix. So if a is similar to C and B is similar to see then ah, similarity is transitive. So a similar to be. And what is that matrix? Well, we know that every matrix is similar to its Jordan canonical form. So if we can prove that the Jordan economic forms are equal, we can prove that um both A and B day is similar to be right and because during canonical forms, air unique, if they're different than we know, that is not similar to be so we really just it's it's comparing the Jordan canonical form. So we really just have to find two different Jordan canonical forms, and that's about it. So to Ah, distinguish, let's make a red and be blue. Let's start. Well, um, to start, we need to find the Eigen values, right? Those are gonna be on the diagonal of the Jordan canonical form, and we know off the bat. If we find the Agon values of both A and B and they're not the same, then they can't have the same Jordan conical form. So a finding Eigen values well, we have our general determined of a minus slammed it I to get the characteristic polynomial and said it to Z So a minus. Linda, I that's determinant of that. And remember how to take determinants of three by three major cities. We, uh, take this, multiply it by the determinant of this, take this, multiply the determinant of this matrix, which is gonna be zero, because zero multiplied by anything. Zero. So we don't count that. And then we add this times the determinant of this matrix. All right. Perfect. So let's go do the red one first. Well, that's just gonna be three. Minus lambda times. Tu minus lambda signs five minus lander. Right. Because vote these terms are zero. And now, plus four times old. Zero time zero on, then minus minus four times two minus Landis or times four tons to minus Lander. All right, And that's just gonna be our determinants. They were going to sum this up. That's going to equal. Well, let's just write a town three minus slammed, Uh, two U minus, land. Ah, five minus lambda plus 16 times two minus. Landau. So that's plus 30 to minus six. Jean Lambda. Okay, Perfect. And we want that equal zero. All right, so I'm going to go ahead and skip this. Ah, Skipper, reuniting this polynomial into a cubic function. I'm just gonna right the cubic function. I'm gonna pause the video and go and calculated that. Just you guys to dio the, um, algebra. It's not super interesting. Okay. All right. So, as you can see, have ah simplified this down. I multiplied all this mess out and got it into this form, which then can check is equivalent to this which gives us the Eigen. Values were right in red because reason grant for a will say land. Ah, there two of them. Lambda One equals negative one that has a multiplicity of to and land two equals two, but the multiplicity of one Okay, now doing the same for B one. Too many ease determinant of Well, okay, so be is an upper triangular matrix, so you can check that this is true. But there's the room that states that the determinant of an upper triangular matrix is just going to be the, uh, diagonal multiplied down. So it would be negative one times negative. All intends to for B, but we're interested in the determinant of B minus lambda I. Which means it's that, but minus Lambda I for each term. So we'll see pretty immediately that that gives us Well, it's negative. One minus lambda squared times two minus lambda. We set that to zero. Well, that is exactly the same equation. Boring Cem minus shine minus sign flips, Which don't matter because negative zero equals zero. So we get the same thing that, um, he has to Oregon values Lambda Wan equals negative one. The multiplicity of to and lamb did two equals two with the multiplicity of one. So we don't have enough to ah, enough evidence neither confirm nor deny that these two Major Caesar's somewhere. They certainly have the same Eigen values. But, um, I need to figure out their full Jordan canonical form. Okay, So to do that, we need to determine the number of, um, Jordan blocks that they each have, so they can have ah, either one or two Jordan blocks for their corresponding to their first there. Lambda One equals negative one, because has a multiple Steve too. So if if they're to Jordan blocks and we know there has to be one Jordan block for lambs to if there to join blocks, that means the matrix is not effective. And this one is defective, and one is non defective than that is proof that they're not similar. And otherwise they have to have the same number of Jordan blocks. So there, Jordan economical forms are equally at IATA. We'll go through all that concrete, Lee, but we have a serum. It states that the dimension of the Eigen space for a noggin value So the number of linearly independent Eigen vectors were concerned to you with Lando one. So, um, if the we just need to be, we need to find out the number of linearly independent Eigen vectors for the given Eigen value in question, and that is going to be equal to the number of Jordan blocks in the Jordan canonical form matrix for the given hide and given Eigen value. Um, that's just a theorem in the book. That's generally how Ugo about it, there is another trick, but, um, we actually won't need it because they're only two options here. Um and so just finding the dimension of the Agon space will specify uniquely a Jordan economical for matrix. And we'll see that I'm just giving a precursor. Okay, So finding Eigen vectors Well, we're ready on B, so you might as well just keep going with the blue. So, um, we need to solve the That's in a So, if the vector equation beam honest, lend ones B plus plus, I time something the B and yeah, C B equals zero. So what does that look like? Well, ah, people a slam toe, I that's just going to be scroll up to R B. It's going to be pretty forgot. So it look right? Yes, it does, because we're just adding one along the diagonal weaken set up in, uh, augmented matrix to solve this. This is just a system of equations, basically, for the components of the could set that equal to zero. Okay, now, this is a pretty easy one to put into, um rare reduced echelon form. You just erase that because it's when you're multiple of this and we flip this sign and we're perfect. That is Ah, wait. Sorry. Not quite weekend at three times this to this. Here we go. OK, so what we get here is that Ah, you actually don't need to solve this for V. We just need to know how many linearly independent V's there will be. So, uh, there is one free variable. So that means that, uh, v b well, equal Alfa the free variable time some vector called vb prime. And there's only one free variable, so there can't be another waas paid. Ah, the B double prime right There just has to be one. So there's only one linearly independent vector. The dimension of the Agon space is one. Okay, so now let's check for a So is going to be going to set up the same idea? All right. A plus one down the diagonal. That's for three night of four. You know I was here. Negative. 44 000 This one is also pretty easy. Um, the first and last row are multiples of each other. 00 Then we can divide out by four and three, respectively. Just guess 111 Okay, Now we can see the same deal here without really solving this. We just have that. Ah, this last row and know what the row is. All zeros. So he a is going to equal some Ah, we call it Alfa A. Just distinguished that from the ALF above l a times B a pride. So it's just gonna have one linearly independent item value wagon vector for its ah, again Eigen value of negative one. Now we'll see that we've actually just proven that is similar to be, But let's right out. Or Jordan canonical forms first. So J a Well, that's just going to be, um, the again values on the diagonal, right? Strong, economical form. Ciro's underneath, and then we need to know where to put the ones on the super diagonal. And we know there can't be a one here because you can't join two different Eigen values so that zero. You know, there has to be only one Jordan block because there's one linearly independent, um, like in vector for negative one. So we joined them together, and that's it. And J b we're going to see is the exact same thing for the exact same reasons. So J b also equals this. Where is my There? We go Equals colon. Okay. Perfect. So we can see that J equals J B. And because A is similar to J A equals J B, it is similar to be you can sort of Ah, in Canton eight. This part all into a is similar to be. Now you have it. That's your proof. I hope this was helpful is a fairly common form of quest.

Okay, so here we again are having a list as input, and we're trying to find the largest even interview. So well, color our algorithm, uh, large even. And the input here is going to be a list, right? So we'll have our list of integers. And as in the previous examples, we will you read them with is a little too and then So these are our integers, and this shouldn't be in empty list. So we also want to specify that and should be at least equal to one. Okay, so they're gonna have a few counters, right? So we'll send k equal to zero. And this is this is just going to keep track of the index or the location of our largest even number. And then we'll also have. I'll say I'll say J Okay, this is gonna be the value, are the largest, even integer. That's when you start the Mets zero. So if it goes through the whole list, it should be returning a zero, right? Since we want to set these storm off at zero, okay, and they will say, Well, four it's reading out that words afore I in our arranging indexes that's going to 0 to 1. All right there. So for one to end for eye in the range of one two are in next end. We need to check a few things, Andre. So first of all, Ah, I I needs to. Even so if if it's even, and you could do that by saying you know there's no remainder when it's divisible by two divided by two of us and only doesn't need to be even it should also be larger than our J value, right? So and I should be larger than whatever current largest, even number is. Well, they will set, said J. Equal to a ice that's keeping track of what our current largest value is. We're also going to set okay, equal to ay, right, says the index that were at the location of this largest number. And at the end of going through all of these, well, the point was to return the location rights we want to return Okay, which is the location of it. But we're using

Everyone. So ah, problem we're looking at today gives us 23 by three major cities and it asks us to figure out whether or not there's similar using their Jordan canonical forms. So because, um, similarity is in equivalence relations, so it's transitive, and, um, the every matrix is similar to its Jordan canonical form. We did some problems finding that transformation of similarity. You know, the s In various times, a times ass equals J. You know, um, so if they're joining canonical forms are the same. Then they will be similar. And if they're not, then they will not be because the door in canonical forms are unique. So it couldn't have two different Jordan canonical forms. It was similar to Okay, while I made that a lot worse. Sorry. Foods. Okay, So what do we do? Well, we just have to find the Jordan canonical form of these two matrices, so let's start with a I want to note a in red swivel future reference. Uh, okay. We're going to need the alien values right to find the Jordan canonical form. So, um, like, in values, they're going to be What did I do that so are Eigen value creation is a T minus lambda. I take the determinant of that and said it. Zero on Sulphur Lambda. So what's the determinant of a three by three matrix? Well, it's going to be, um this multiplied the by the ah determinant of this two by two matrix, right? And then plus this multiplied by the German of this two by two matrix starting on the right side, that's important. And, ah, so forth with this and this going to erase all that clutter because it's not nice to look at. Um, also, you'll notice that if we multiply zero by the determinant of that last blue matrix, I did. It's just gonna be zero checks out. Um, okay, so we're just gonna have to sums. Let's do it out. Seven times. Five times six minus zero time zero. So seven times, five times six. That's well, um, but on six is 30 times seven is 210. That's cools to 10 0 I'm so sorry. That is supposed to be. You have to do r minus land. This really not on it. Minus slammed its right. So it's seven minus landed times five minus lander Times six minus Lambda seven minus Lambda Times five minus Landau. I'm six minus lander. And then we need to some the next one this next term that I drew in. Uh, believe green. So it's this times the determinant of this matrix starting at the right. So it's one times zero times one. So one times zero plus negative native one time six. So one time, six minus lambda. It's minus limbs. So, uh, plus six minus. That's gonna be equal to zero. He did assault that. Um okay. Yeah. So we have zero equals six minus wind up times. You them? I'm just distributing out time. Some one plus seven minus slammed. A times five minus lambda. You can see right off the bat. Lambda One Bqool six. And we'll wait until the end. Right there. Multiplicity, ease. So we can just erase this. We've already accounted for its possibility, and now we have this. Okay, so what is, um, seven minus landed? Times five minus Lander, That skin G equal to 35 35 minus seven minus five. So that's Ah, minus 12. When, uh uh Plus, when I'm just squared and then we ever plus one. So let me just make this a quick 36. All right equals zero quadratic equation. That that's Lambda equals 12 plus or minus square. Roots of hope squared is 1 44 minus four times a is one time, See is 36 4 times 36 is going to equal once again 1 44 So this is zero. So this term cancels out over two. So am D equals six. And that is why we, ah, waited for a month lettuce ity, Multiplicity. Because we actually have that. The multiplicity of six is going to be three. So every Eigen vector is, um it's just gonna be six. That's the only Eigen vector. Okay, so now we need to take the, uh, figure this out for B two. Because if the Eigen vectors aren't the same, then we automatically know the Jordan Canonical forms aren't the same. And you'll notice that bees and upper triangular matrix. So everything below the diagonal zero you know that the determinant of ah, an upper triangular matrix is going to be I just did the diagonal elements multiplied together. So be congee O and B minus, uh, B minus Lambda I determinative. That is zero. What's feminine with that? It's not betraying your matrixes. Just six finest lambda do the third equals zero. So again, like in a lambda equals six and the multiplicity is going to be three. And that sort of expected would be pretty boring if this was just an ID value problem. Um, so the next thing we need to look for it is the number of Jordan blocks, which is going to be the same as the dimension of the Agon space. In this case, there's only when I can value for each So we can say that, General. Um Okay, so well, we're ready on beast. Let's just go and do it for be, um So how do we find Eigen vectors? Let's be minus slammed. Uh, and Lambda Weaken Writers six. Because the only thing you want to slam the r times V zero so we can set up in resolving for beak so you can set up an augmented matrix to do that B minus six. I Well, that's just do this, but replace these sixes with six minus 60 So B minus lambda. I, um that's going to be something along the lines of Don't know. I treat that big 000 Let me check. This is important. Negative. 110000 You want something multiplied by that? Really zero. So we can just immediately see that there is going to be, um we don't care about the Eigen vectors. So we really don't care what this actually says. We just care that there are to free variables And so there will be two possible Eigen vectors, right? Because there is a you can write V as a times B one plus B times V to where the free variables are represented as ones in V one and V two. So there are didn t equals two. There will be to Jordan books. So, Jim, you're doing the blue then? Yeah, calls to All right, So let's do the same thing for a now, looking back to a So we need that a a minus six i times V That's p equals zero, and we'll make this a double you just to avoid any confusion because used fee for be Okay, So what's a minus six? I it's gonna check. That's going to be one negative 10 along the diagonals. Everything else the same. So one negative. 10 Then check. Negative. 111 Going to do the same thing. Give it the same treatment. And right off the bat we can see that these two are opposites. We can add them together and we get something that looks like 110 Okay. And we can subtract this so we can just brace that and put a zero there because we can subtract thes two rows and we get the results. There is 13 variable here. And so we know that the dim a straighten this out then. Sorry, Didn't e where it's the Agon space. Okay, is going to be equal to one because there's only going to be one vector. Ah is linearly independent. That is going to be it's it's going to be v w equals just any times w one right where the three vectors one w one. So because dym e for a does not equal Demi for B means the Jordan canonical form for B will have a different number of Jordan blocks, namely joined canonical form for B will have to whereas performed for A We'll have one. So what does that look like? That's suit and red that it looks something like this for a and for B that would equal like this. All right. There are two blocks in the blue and one in the red. So we have This does not equal this and a is not similar to be all right. I hope that was helpful. Everyone. Good luck out there.

So here we are, given that metrics is a physical seven, two -3 and nine. And matrix B is equal to B two -3 and five. And it has given that a bicycle B. Therefore, we need to find out what is using. Matrix multiplication first. We need to find out what is A B. So maybe will be equal to 70 minus six, mm plus 10. And negative three P minus 27. And negative six plus 45 is equal to 70 -46 and 14. Palestinians, -3 p -27 and disease 39. That is a physical. Similarly, we can find out what is busy, sorry, B. B. A. Is equal to 7 to -6 two B -2 plus 18, -36 and 39. So since it has given that A B is equal to be a weekend equated element, therefore -3 P -27 is equal to -36. That is three people. Us, 27 is equal to 36. Therefore we get pc. Will too three


Similar Solved Questions

4 answers
{ Iifi L 0 1 H 3 N | 1 1 VL L 1 W 0 8 L H f [ L
{ Iifi L 0 1 H 3 N | 1 1 VL L 1 W 0 8 L H f [ L...
5 answers
74) A0.136 g quantity of acetic acid is dissolved in enough water to make 75.0 ml of solution. Calculate the concentrations of H' , CH;COO , and CHGCOOH at equilibrium. (K; for acetic acid is 1.8x 105)
74) A0.136 g quantity of acetic acid is dissolved in enough water to make 75.0 ml of solution. Calculate the concentrations of H' , CH;COO , and CHGCOOH at equilibrium. (K; for acetic acid is 1.8x 105)...
5 answers
Hedunibip{LE[-/3.33 Points]DETAILSLARCALC1I 4.4.041.Find the area of the region bounded by the graphs of the equations_ Y = 4x2 5, X=0, X= 2, Y = 0Need Help?Read It
hedunibip{ LE [-/3.33 Points] DETAILS LARCALC1I 4.4.041. Find the area of the region bounded by the graphs of the equations_ Y = 4x2 5, X=0, X= 2, Y = 0 Need Help? Read It...
5 answers
Evaluate the line integralwhere C is given by the vector function r(t).F(x, Y, 2) = (x Y2) i + xz j + (Y + 2) k,r(t) = (2 j + (3j - 2t k, 0 < t < 2
Evaluate the line integral where C is given by the vector function r(t). F(x, Y, 2) = (x Y2) i + xz j + (Y + 2) k, r(t) = (2 j + (3j - 2t k, 0 < t < 2...
5 answers
Question 19For the reaction, 2Fe2*(aq) + Cllg) _ 2Fe3-(aq) 2CI-(aq) the value of E"cellis 0.588 V What is the value of E"cell for the related reaction_ given below? Fe?t(aq) + Cl-(aq) _ Fe2t(aq) + %CIz(g)13294 0.294V0ov588 VOSubv
Question 19 For the reaction, 2Fe2*(aq) + Cllg) _ 2Fe3-(aq) 2CI-(aq) the value of E"cellis 0.588 V What is the value of E"cell for the related reaction_ given below? Fe?t(aq) + Cl-(aq) _ Fe2t(aq) + %CIz(g) 13294 0.294V 0ov 588 V OSubv...
5 answers
A baseball team plays in stadium that holds 56000 spectators With the ticket price at Sll the average attendence has been 25000. When the price dropped to S1O, the average attendence rose to 28000.Assume that attendence is linearly related to ticket price_[hat ticket price would maximize revenuePrevien
A baseball team plays in stadium that holds 56000 spectators With the ticket price at Sll the average attendence has been 25000. When the price dropped to S1O, the average attendence rose to 28000.Assume that attendence is linearly related to ticket price_ [hat ticket price would maximize revenue Pr...
5 answers
Which of tbe follewivg 4i2 Subspces 2f with 4su./ obetatsms lutax R} Sp {'+X ) '+x7 $ Sr {1,x) x', x' } s %
Which of tbe follewivg 4i2 Subspces 2f with 4su./ obetatsms lutax R} Sp {'+X ) '+x7 $ Sr {1,x) x', x' } s %...
5 answers
Evaluate the integral 22 p6" 8) dx by making the substitution & 24 8NOTE: Your answer should be in terms of € and not U_
Evaluate the integral 22 p6" 8) dx by making the substitution & 24 8 NOTE: Your answer should be in terms of € and not U_...
5 answers
23. ilso-VJdr24 . J[skx)-3]dx
23. ilso-VJdr 24 . J[skx)-3]dx...
5 answers
(Round to four ducimal places 38 noeded ) Sial0 Iha conclusion;Ho: TheroJuficient avidanco to aupport the claim Ihot Ihe now cereal lowors lotal blood cholostorol lavelu
(Round to four ducimal places 38 noeded ) Sial0 Iha conclusion; Ho: Thero Juficient avidanco to aupport the claim Ihot Ihe now cereal lowors lotal blood cholostorol lavelu...
1 answers
Use the property named to complete each of the following statements. The square roots property: If $x^{2}=y \geq 0,$ then______
Use the property named to complete each of the following statements. The square roots property: If $x^{2}=y \geq 0,$ then______...
5 answers
The synthesis of vinyl chloride from ethylene and chlorine ga5; HzCCHzlg) + Clzlg) H;CCHCIg) + HCIg) and the following data collected:TrzlHzCCHz (M) 0.150 0.150 0,300 300CIz(m) 0.090Rate (M/s) 2.41*10 2 4,82 * 10*2 1.92 * 10-! 4,82 * 1020.180 0.3600.,090The reaction is(Select |order in cthylene[select ]order chlorine andSelect |order overall
The synthesis of vinyl chloride from ethylene and chlorine ga5; HzCCHzlg) + Clzlg) H;CCHCIg) + HCIg) and the following data collected: Trzl HzCCHz (M) 0.150 0.150 0,300 300 CIz(m) 0.090 Rate (M/s) 2.41*10 2 4,82 * 10*2 1.92 * 10-! 4,82 * 102 0.180 0.360 0.,090 The reaction is (Select | order in cthy...
5 answers
Graphthe function g(X) = 4^x+3 and give its domain and range
graphthe function g(X) = 4^x+3 and give its domain and range...
5 answers
Find the area of the portion of the paraboloid z = x^2 + y^2that lies inside the cylinder x^2 + y^2 = a^2 . Also find thevolume between it and the xy-plane.
Find the area of the portion of the paraboloid z = x^2 + y^2 that lies inside the cylinder x^2 + y^2 = a^2 . Also find the volume between it and the xy-plane....
5 answers
LLueatdRolor Io lhe {gute belaw Io brd Ine brtenmeaanan
LLueatd Rolor Io lhe {gute belaw Io brd Ine brt enmeaanan...
5 answers
The reaction was commenced with 414 mg of salicylic acid (138 g mole) and 0.3 mL of acetic anhydride (102 g/mole: d 1.08 g mL) After crystallization 378 mg of aspirin (180 g/mole) was obtained.Determine the limiting reagent and calculate the theoretical yield. (show Your calculation)Theoretical Yieldm2g Limiting reagent_ Calculate the percent yield (show your calculation)
The reaction was commenced with 414 mg of salicylic acid (138 g mole) and 0.3 mL of acetic anhydride (102 g/mole: d 1.08 g mL) After crystallization 378 mg of aspirin (180 g/mole) was obtained. Determine the limiting reagent and calculate the theoretical yield. (show Your calculation) Theoretical Yi...

-- 0.027153--