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Let $A=\left[\begin{array}{rr}{-2} & {-3} \\ {6} & {7}\end{array}\right] .$ Repeat Exercise $5,$ using the following sequence $\mathbf{x}, A \mathbf{x}, \ldots, A^{5} \mathbf{x}$$$\left[\begin{array}{l}{1} \\ {1}\end{array}\right],\left[\begin{array}{c}{-5} \\ {13}\end{array}\right],\left[\begin{array}{r}{-29} \\ {61}\end{array}\right],\left[\begin{array}{r}{-125} \\ {253}\end{array}\right],\left[\begin{array}{c}{-509} \\ {1021}\end{array}\right],\left[\begin{array}{r}{-2045} \\ {4093}\end{array}\right]$$

$\lambda=4.0024$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 8

Iterative Estimates for Eigenvalues

Vectors

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okay. In this question, we want to approximate the Ivan value and Victor's off this matrix. Given that we know X is equal to 11 a X is equal to minus 5 13 Bolivar a five x, is it too? Negative? 2045 4 1009 3 The first step that we do is we can reschedule this, and it will still be an iron. Becca, you for the 93 One minute to zero or five. Or mine three. And that is simply negative. 0.4996 and one. So we can just forget about this number right here because we're only talking about We're talking about Iran vectors. And if you scale this by heart 4000 and 93 it's still gonna be the same. I've been better. So now we haven't I convict that right here. Have I been Victor with one in the second entry? And so it's an approximation often island Victor off, eh? So it's you compute the argon value. Just remember that a me using to land a B so just simply computing baby musical too negative two minus 36 seven times by natives Their point for mine. 961 This is equal to negative 2.8 for 00 to 4. Well, quick. So remember that this is Lando V. So it's just landed times with this land on time by one. So this is equal to something in it doesn't really matter. And we have landed times one. So that's just Lamba. So that so that I can values. He sent me this Lamba. He's equal to pull 1002 for approximately

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