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Question

Is $\left[\begin{array}{c}{-1+\sqrt{2}} \ {1}\end{array}ight]$ an eigenvector of $\left[\begin{array}{ll}{2} & {1} \ {1} & {4}\end{array}ight] ?$ If so, find the eigenvalue.

Amy Jiang · Accepted Answer

Okay, so we&#x27;re asked if the following is that? I get back there to one. What? Four. So it&#x27;s more to play that together. So we have negative one plus skirt too. And one. What does that give me? That This gives me a negative one. Plus juice. Go over it with two in three plus group too. Okay, Now, let&#x27;s multiply. Dream Plus screwed too. With our first don&#x27;t you hear? That gives me *** three plus two plus a visit. It&#x27;s negative. One us to skirt too. Okay, So since I&#x27;m want to play this together and this actually matches are furs and G of X, we have negative one of courage to and one as in Aiken back, they obey. And that corresponds to the Alien Valley in three plus two.

Amy Jiang · Answer

Okay, so we need to determine if these and I really at the bowling tricks. So what&#x27;s the aim? When history I There he gets 1 to 2. Three. Negative to one. There are 11 minus three times our identity. So that&#x27;s 30 zones or three, Joe. Okay, that gives me to do too. 35 negative. 51012 joke. Okay, Now, let&#x27;s reduce this with zero. So he gets, he was he was going to go three, ***, 510 And no one there were 20 Mr Loses to one than the one that 10 No one better to zero and Jill to four. So and when the time you get 1030 they&#x27;re all one that tunes girl until it&#x27;s also so Okay, So this actually has, uh, a non Jew of your solution. So based on this are three isn&#x27;t again. While you

Rakvi . · Answer

just kill. Clear did remain on and off a minus 4 g. I This is a three by three matrix whose first entry is three minus four, which is negative one. It&#x27;s second injury is zero, and its third entry is negative. One similarly right. Indonesian every in tribute. Okay. And this system nineties, you can just expand along first rule, and you will see it is a cool do negative line times negative one minus four minus for negative one. James, you, which is a qualified minus 50 Okay, so, yes, claim that isn&#x27;t a gorilla. And you want to find one corresponding it Eigen Vector. So just solve this equation. Airy equals or even better rather than solving the equation. Well, again, Victor is nothing were Oh, Victor. Okay, that satisfies this equation a minus for a games. We should be zero. Right, Because the Magan victories a vector visas that eight times three is equal to 100 times. So this is our metrics in minus four time. Say, just find a victor in a small space. So we&#x27;re solving or Victor Extra Next week&#x27;s three. That sentence place. The equation equals zero. Okay. Yeah. Okay. So let&#x27;s start solving the crazy. So the first centry gives us negative X one minus X tree equals zero. That gives us the relation. That ex tree is negative. Excellent. Okay, the second entry gives us the equation two times X want buying is extra. Classics tree should be zero, Which gives us since x three is negative off x one. Okay, so this gives us that X one should be equal toe extra. And the third, uh, entry gives us minus three x one less for extra. No sex tree equals zero They should give us. Since X one is equal to extra. This just gives us extra place x 30 which is true because extra is excellent and excusing. Do fix. So this doesn&#x27;t give us any new relation. Okay, so we have. So are victors. All the Agon victors are off this form x one, and then extra is equal to x one. And the next three is negative. Affects one, so you can just use one wagon. Victor, Toby. 11 Thank you, too. That&#x27;s when I got

Amy Jiang · Answer

Okay, so let&#x27;s multiply. 367337565 With our given value one negative to one. You can see this is equal to *** too. For negative too. That&#x27;s just a multiple of our first, like, two times, 1 to 1 So we can see that this isn&#x27;t I connected, and we haven&#x27;t even value of

Sarah Klein · Answer

this problem asks ist friend Eigen. Values of the Matrix A with the given Eigen vectors could do this using the equation. A times V is equal to Lambda Times e So first for the first Eigen vector V one, you can plug in a 4213 then V one vertically. One negative too is equal to lambda Warn times one negative, too. Then doing matrix multiplication on the left side, we got the top row to be four times one, which is four plus one times negative two, which is negative two and two times one which is two and three times negative two, which is negative. Six is equal to to negative four and that is equal toe lambda one times one negative too. So we could see the constant Lambda 11 Dividing to divide by one and negative four by the bynegative two gives us land. One is equal to two. Then for the second Eigen vector view, too, we can plug in again a 4213 Then the vector V two wishes 11 is equivalent to lambda two times 11 again matrix multiplication of the left side, The top row. We get four times what it&#x27;s for. Last one times one, which is one 1212 plus three times one is three, which gives us 55 which is equivalent to land a to times 11 that if we divide five Vector 55 by the Vector 11 We find that landed too is equal to five, and those are two Eigen values.

Rakvi . · Answer

Let&#x27;s just start and multiplier Victor with the matrix and see if you get a multiple of the vector or no, you. So first rule is this, and our victor is our second rule is and the total is so when you multiply, we get that the first gentry off the three by one vector is zero do and and the strange across very four year. So the second entry should be minus 16 plus 15 plus one, which is zero. I&#x27;m so sorry. This is the and the third entry is it minus trail, which is negative for past 40 Okay, so So this depends on your definition off Eigen value. If you force that your Eigen value should be non zero, then this is not equal to lender times or negative 31 for any non zero, Linda, because ofcourse, Lambda has too busy. But if you include your lender to zero in the definition, then you can say that this is an Eigen vector with zero as a ***. So I would recommend Just look back in the textbook and see what their definition of wagon value is worse. A second victor, if they include Aiken value Toby zero than it is an argument

Problem

Is $\left[\begin{array}{r}{4} \\ {-3} \\ {1}\end{…

Problem 4 Medium Difficulty

Is $\left[\begin{array}{c}{-1+\sqrt{2}} \\ {1}\end{array}\right]$ an eigenvector of $\left[\begin{array}{ll}{2} & {1} \\ {1} & {4}\end{array}\right] ?$ If so, find the eigenvalue.

Answer

The vector $\left[\begin{array}{c}{-1+\sqrt{2}} \\ {1}\end{array}\right]$ is an eigen vector of the matrix $\left[\begin{array}{cc}{2} & {1} \\ {1} & {4}\end{array}\right]$ corresponding to the eigen value $\lambda=\sqrt{2}+3$

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Linear Algebra and Its Applications

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The vector $\left[\begin{array}{c}{-1+\sqrt{2}} \\ {1}\end{array}\right]$ is an eigen vector of the matrix $\left[\begin{array}{cc}{2} & {1} \\ {1} & {4}\end{array}\right]$ corresponding to the eigen value $\lambda=\sqrt{2}+3$

Linear Algebra and Its Applications

Lily A.

Catherine R.

Heather Z.

Kayleah T.

Vectors Intro

Vector Basics - Example 1

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

Lily A.

Catherine R.

Heather Z.

Kayleah T.

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

Linear Algebra and Its Applications