is-lambda2-an-eigenvalue-of-leftbeginarrayll3-2-3-8endarrayright-why-or-why-not

Question

Is $\lambda=2$ an eigenvalue of $\left[\begin{array}{ll}{3} & {2} \ {3} & {8}\end{array}ight] ?$ Why or why not?

Rakvi . · Accepted Answer

So we just want to check whether lambda satisfies the equation. Determine on and off a minus, Lambda I or not so trim. None of a minus loved. I is determinant of this matrix minus lander names I, which is Lambda 00 Roland, this is a quarter determine and off. Three minus lender. Oh, three. And if my Muslim and it&#x27;ll not of this two by two matrix is just three minus. Lander names. Eight minus. Landau minus six. Okay, now, if I substitute land, I could do in this. I get three minus two. I&#x27;m ST minus stool minus six, which is equal to Zito. Solando satisfies this equation. So yes, Land I Quito is an and really 20.

Amy Jiang · Answer

Okay, so we know that, uh, mom, because you could not go too well. Maybe a nagging relative, Elif. Enough. Enough. It satisfies equation. A accident with the negative to X. But that&#x27;s the same as a plus two I Times X is a good result. So, what is a plus two? I That&#x27;s this. 733 negative. One plus 2 +01302 What is that? That&#x27;s just 9331 And we can see that our columns are linearly dependent. So this is what this is gonna have a nontrivial solution. So we can say that, too, is and I get value.

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

So we just multiply the big the vector with the corresponding matrix and see if this is equal to a multiple of this vector or not. I love matrixes this and our victor is. And if you multiply, we get minus three times one, which is minus three plus four and second entries minus three Danish one plus 32 it turns for and this is a quarter to one. And the second injury is 29 which is not equal toe multiple off the vector one for so 14 is not an Eigen Victor for this metrics.

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

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

Problem

Is $\lambda=-2$ an eigenvalue of $\left[\begin{ar…

Problem 1 Easy Difficulty

Is $\lambda=2$ an eigenvalue of $\left[\begin{array}{ll}{3} & {2} \\ {3} & {8}\end{array}\right] ?$ Why or why not?

Answer

Yes

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

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

Linear Algebra and Its Applications