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Diagonalize the matrices in Exercises $7-20,$ if possible. The eigenvalues for Exercises $11-16$ are as follows: $(11) \lambda=1,2,3$ (12) $\lambda=2,8 ;(13) \lambda=5,1 ;(14) \lambda=5,4 ;(15) \lambda=3,1 ;(16)$ $\lambda=2,1 .$ For Exercise $18,$ one eigenvalue is $\lambda=5$ and one eigenvector is $(-2,1,2) .$$\left[\begin{array}{ll}{2} & {3} \\ {4} & {1}\end{array}\right]$

diagonalizable.

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 3

Diagonalization

Vectors

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Okay, What is a minus? Lambda? I That's two more is Lambda Three for one month, Islam, that now let's take exterminated that to get the characteristic Well, you know me up. That gives me No! Do you like London? 11 is long. The and minus three times four that simplifies to land the squared minus three Landa minus 10. Excuse me. Land them when it's five times on the plus two. So our alien values are *** two and five. Okay, let's start with Monday is equal to five. So you met in a minus five? I Yeah. This is equal to negative. 334 Negative. For so seeing this is the stewardess multiple to shutter, right? They seem to be a factor. Or the values 11 multiplied by three. Or a negative 11 What? Deployed by three. And then multiplied by negative four. So we get that on. General solution is to 11 So Orion space is just 11 Okay. Now for that landed, you could too. Negative too. It's all for that. We got a plus two I that's just equal to 4343 We have another repeat. So we have that little boys do for three year old Joe. So we get that X one is equal to They got three over four. Next to an excuse free. So our general solution becomes X two times negative. Three over four one. So are again space for this one is negative. Three over 41 What? But simplify that. Or make that it's a whole numbers. So we get this in the other three times four. Okay, Now it's construct to again, um, spaces. So that's this. What did we have? 11 in the 34 and our that. I got a delectable matrix 5002 where five has this matrix or has that again factor. And you go to your house this

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