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= 1 lowcng ofth colutiont (Sucroes tngoltileCuHa...

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= 1 lowcng ofth colutiont (Sucroes tngoltileCuHa

= 1 lowcng ofth colutiont (Sucroes tngoltile CuHa



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$\left[ \begin{array}{rrr}{1} & {2} & {-1} \\ {0} & {1} & {1} \\ {0} & {-1} & {1}\end{array}\right]$

This problem will be to determine explanation regions each of power a. T we're a excuse me tricks Cubans here. So there's so much of this problem is done in two main steps. The first step is to find a generalized idea in Victor's Off the matrix A to determine the fundamental matrix X t And then we will use this formula here to compute explanation. So let's start. So we need to find first the eye gym bodies I can values are given by find First off A, which is the determine off the matrix a minus R types that entity which to return of rejects one are one, 21 sergeant one term in office matrix is keeping bythe are three plus three It's for these factors Hi Directive Our plus one times our minds choose So then we need to make this equal to serial five sports That first solution given by this bracket people zero so are equal to its form. Second solutions conveyed this bracket bracket, but zero so are you. So we also need to take into account the multiplicity off each item about this bracket. Here are my our boss one has exported while they're here, they're placing the Fuze I am. Value is just one on Pierce ones in these factories. On the other hand, the idea of value are equal to chew. Appears twice so therefore, commit complicity off these. I hear you. So we need to take this into a calm to find the general ice age in gloves off the rejects. So let's find the IJ in Victor's after Richard's A. So the first line for I think most pace off inmate traits A plus, I So you see, for our equal that this matrix is the major scale to one 2 to 1. Cyril. Okay. Okay, so this is quite willing to dominatrix one Cyril cereal 12 Sure. So there's no space of this matrix is generated by the victory you have won. That is 34 So this is our first general. It's a joke. So remember that they want to place a t of thes ie in by you. So the molars pays needs to be one in this case, but these does what? Okay. On the other hand, look at the next item value are equal to you and a So this is the matrix. You got four children. Syria. Individual. So the competition of the noticed face off these past that nature most peace you can do you If you want to compete yourself, he's hopeless. Okay, so remember the multiplicity of this I Wow. So this knowledge space is not a generalized I thank you off our eye about because you mentioned a mention of the No space is not the same husband off 10 minutes. Finding more space off the matrix. A minus. True. I escort this squired power here is the same as the multiplicity. Both our idea. Thes magics, squirt. He's the maid. Breaks given, then by great tricks. Three big tree tree four for four. It is a cooling to the matrix one production and this nose based bus half two generators. So the 1st 1 he's Cyril sickle one three. So they tell you why from the agent are these? I don't think those are two children. Allies ij inspectors to that charming and matrix ext. Okay, so the matrix X t is the hatred skin, then treacle x one T x to t x three. Okay, so this these columns each of these columns come from eats generalize idea. So let's find first, then x one of t that comes from the agent already before. And this eye you, Dexter. Negative tree for thes kahlo is giving thing but into the power teat Times tree for so things to make tea here comes from this Let's find the next trip so x too cheap com agente are equal to do you, Doctor, You're Jewish one Ciro. So remember, this is the inspector come from the normal space with the matrix A minus two. Okay, so he's not a regular i ice agent Victor that comes from these non space in this case. Then this'll calm will be the matrix, given by each to tee times plus team times a true t they think a wings to I. So we need to find them. The implication of this matrix thing tax you choose. These terms depended. So this will be easy to t means defector. Why, Cyril one Which the Victor Jew Cyril Ciro T h t The identification of this matrix times He's the victim's shoe. So we get us a result. Yeah, e t he to achieve waas t t. All right, so let's do then X three seem lurched off. One. This will be eating the power to t the victory three plus tee times to t A minus. True, I That's your trees, old sergeant. Allies No. One case. This would be to tea things once. One times it's your wife. Why? And again, this is each report to G. T. G. So we can write down our from the mental tricks. Asked the magics x t quite cheap tricks. G g Cheers for tea achieved. Plus, she keeps calling to cheer t each team to poet e T minus the h g way Need to compute the inverse off this matrix Emma Lloyd a t e contest. So wait, this magics reaches found t e quanto 00 we get in matrix one for you in the Matrix for the Regis four. It's in birth matrix off fighters. That, then, is to multiply his big things here on the embers. When we do these with the kitchen's right there, whole missus, your final answer will be three h t that suits you team first roll. It's plus for T six. You get for tea for five here lines for tea plus 13 Tiu here. Keep me too. 60 Jury team T team. I will be true. T I must take Tiu the fire.

So here we have a big Five by five Matrix, and luckily, we are going to use software to do the heavy lifting for us. Okay, so this is our given five by five matrix here. Okay? And so we put this into some sort of software that will find Eigen values, and we get that the Agon values are one 11 eye and negative. I okay. And then we put it into, Ah, another algorithm that will give us the vectors. And those are the first time was just one of the top and then zeros. Next one is just a one in the second place. The 3rd 1 is a one in the third place. It is a little bit excited. It's not gonna be an identity and tricks. There's an eye there. And then we also have, um, one and negative. I Okay, so these there are i n vectors. So, um, now we can also get the big x of t from this, and so it's going to be really big. Um, can it gross monster? The matrix here, when minus t plus one have xi squared. He's a t 1/2 xi squared. U t t plus 1/2 t squared either the tea 00 t minus t squared. He didn t one minus t minus t squared either. The tea plus two squared into the tea. Ah, here we would have negative three t minus t squared he to the t can t squared. I don't have t squared e to the t um t plus 1/2 a t squared. He didn t and one plus two t plus 1/2 a t squared times e to the t. Okay. And then we just have this Lessel corner to deal with. And so this is gonna be our co sign of tea. Scientist e negative sign of tea and co sign of tea. Okay. And so then we evaluate the, uh, the X zero. Really lovely thing happens. All their teas go to zeros are signs go to zero. And when you cook it out, we actually get the identity matrix said just ones across the diagonal. And that means ah, that the inverse is also get any matrix. So when we go to calculate, he'd, uh, big a t being equal to this exit. Tee times are in verse at zero since the M percent zero. Is it any matrix? It's just gonna be equal to Exit T. So we already figured that out. There is nothing left to do. And the answer is this big guy here.

We want to solve the friendship equation. Exhibition ski equals the metrics A but employed by AEG circle. First we give the egg and values and the angle vectors of the metrics air. We can get the Eigen values of the metrics eight by putting the metrics here one to minus one. You won one zero minus 11 and we subtract all which is our values. From the diagram of these metrics minus four. My ar minus are. Then we equate the determinant of these new metrics to zero. We can use the third rule the equation. Oh, these determine we have the science convention here. We have lost minus plus. Then we have zero gives zero the first of the secretary minus one and we multiply it by the permanent minus one. And we have the negative sign minus one, then with the booster. While tabloid by it. That determinant of the matrix. Why? Minus are minus one zero one. Me Me excluded this from that sermon. Then we have one minus. Are we have less one minus or what? The blood boil The determinant one minus are Then we have one minus are to zero one minus are as we excluded this, but with the metrics and this old equals zero. Now we continue The first determined of the first metrics will be one minus are minus zero will be one minus, or and the second the tournament off the middle of the second metrics, unless one minus are welcome Blood boy one minus are squid minus zero, which is a woman's are few all equal zero. This gives one. Minus are month of Lloyd boy one plus one minus are squid. This equals zero. Which means that the first good off R r equals one or one minus r squared one minus are all the square plus one equals zero, which means we have all one minus are equals, posted or minus Ali, then our equals one most of minus all. Now we have green solution and complex solution off the Eigen values. We can start by their solution. R equals one. We get the Eggen Victor correspondent with this island value, we can do this, Boy, wouldn't the metrics a which is one minus one 011 zero minus one one and we subtract. Or from that they're gonna minus one year minus month minus one and we want deploy this metrics, boy, the again Victor began. Say you want you too you see and quit this multiplication does you? Now we have the original zeros and we can use in two equations off these metrics of the multiplication of these metrics These metrics against three equations who can use any two of them. For example, we can use the second equation which is the multiplication of the second rule by the victor. We have zero mark about by you one give zero and zero multiplied by you to give zero and one look of blood by you three gives you three equals zero which means you three equals e the can use a 30 question zero about the blood by you one and minus one multiplied by you too. Minus two. You cool plus zero maca buoyed by usually gives you equals zero which means that you to So it was you and we can put you want any value. We can put you one equals one. For example. You want nip? Hey, one equals one. Then there we have the Eigen vector corresponding toe all equals one. We have you equals one gonzo and we go. So the complex Eigen values we said this was at R equals one. We can go toe at our equals. Any off the agent complex Eigen values. For example, one of us Oy. And we do the same. We have the metrics. One tu minus one 011 zero minus one one. And we subtract. Or from the magnum minus one minus. Oy minus one minus Y minus one minus Ali. And we must deploy this metrics by the Egan Director that 123 and equate this multiplication to zero again. He was in off the two equations. We can get the first equation from the first true multiplied by the victim. We have minus oy. Tabloid buys it one plus too much obliged. Buys it toe minus one mark. Blood by the three equals zero. The second equation from the second room of the blood by the victor is you plus zero plus minus. Ali buoyed by. Is it plus? Then three equals you from by booting. Then too equals one from the second equation. Here we can get that. The three it was buying us equals it was all And from the first equation you, But getting sick two equals one and three equals Oy, We can get that one equals two minds I invited by which equals minus one minus. Oy minus one minus two equals minus one minus. Roy. Now we have the Eigen vector corresponding that with complex Eigen. Value is in equals. We have Zidler near. Is that one minus one? Minus toy. We have to. We have put the to a close one and we have to be equal. Soy equals minus one 10 Plus he separated the real value and the the import and the complex sport minus two. We don't have from export Insitu, and we have only completes part of the three Good Lloyd by I. This means that here we have the victory and we have here the victor be. And we remember that the Eigen value equals one plus one minus soy. This means we have all four, which is the real board of equals one and better equals one, which is a coefficient of the complex sport. Now we can get the general solution kicks off the will be three terms. One clear for the real Eikenberry on two terms for the complex again varies. The green one equals C one first constant multiplied by Yeah. Does that party have R equals one? Ito the bar rt What? The bloody boy. The Eiken value, which is one gonzo plus The second term is seafood corresponding toe The complex again values about the blood boy eagles of our all for tea we have going on in science 30 And Vidic was one. What? The blood by a minus one one is you Plus Hey, there's a lot of all 30 cause I nt but the boy boy effectively minus 20 on one. Let's see three tabloid boy e a lot of team All 14 I was lying with that you employed by AM minus one 10 minus e a lot of tea. So in the not tabloid boy me, which is join us toe little one. We can simplify the general solution to be X 50 It was C one The boy by the victor Eat the bar 50 The ones you know plus Second gonna see toe employed by the victor into the world of tea. Sci fi minus is ROrtiz 20 minus toe Either the body 50 cause 90 And in about of peace I Inti and either the world of t resign t plus c three month employed by the victor minus into the about of tea cause I ain t bluff to either the war of t 70 e to the power of T cause I ain t And minus e to the power of t So I mean okay. And this is the final answer. Ah.

We want to solve this system of the questions using Go Jordan in ammunition method. First, we exclude X one from the second equation here. We can do this by multiplying the first equation. Oh, you minus one provided by one minus I and we had the first equation toe the second vanquish. First we have the first equation. As it is, the change is only for the second equation. We have eliminated X one from the first from the second equation. And we have on the extra room we have minus two, divided by one minus I my enough When less I these old is multiplied by X two equals you. We can simplify the second equation, Toby. 24 that the minuto You have one minus all you and you. The first thing we have minus two. And for the 70 we have minus when bliss I'm a tabloid by one minus soy, which is one minus I square, which is minus one bye bye x two. And for further simplification, we can have we can about the boy, you know, one minus soy here on here the lift, insight and right hand side. And we have no minus two minus one minus one. Which is you. We have minus two equals minus one and minus minus one, which is 21 plus one. This old is multiplied by X two. Finally, we have that extra room equals zero after we have eliminated X one from the second equation. We can't go backwards to eliminate exit from the first equation here by substituting back by its very, which is you. Now we have from the fittest equation you have eliminated X do may have one minus. I have deployed by excellent equals zero. And to simplify this equation, we can write. Exxon equals zero, and we have the second equation as it is, which is X two equals zero. And this is the final answer off our problem.


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