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In Exercises $1-4,$ the matrix $A$ is followed by a sequence $\left\{\mathbf{x}_{k}\right\}$ produced by the power method. Use these data to estimate the largest eigenvalue of $A,$ and give a corresponding eigenvector.$$\begin{array}{l}{A=\left[\begin{array}{ll}{4} & {3} \\ {1} & {2}\end{array}\right]} \\ {\left[\begin{array}{l}{1} \\ {0}\end{array}\right],\left[\begin{array}{l}{1} \\ {.25}\end{array}\right],\left[\begin{array}{c}{1} \\ {.3158}\end{array}\right],\left[\begin{array}{c}{1} \\ {.3298}\end{array}\right],\left[\begin{array}{c}{1} \\ {.3326}\end{array}\right]}\end{array}$$

Eigenvector $x_{4}=\left[\begin{array}{c}{1} \\ {3326}\end{array}\right]$ or $A x_{4}\left[\begin{array}{c}{4.9978} \\ {1.6652}\end{array}\right]$Eigenvalue $\lambda \approx 4.9978$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 8

Iterative Estimates for Eigenvalues

Vectors

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Okay, So in this question, you want to approximate our Ivan values and Ivan vectors off this a metrix right here. And by the way, So this is a This is really important. So if you want to use it, just use plastic. So this is a matrix right here on the day of that is given to us is zero is equal to 11 x zero x one is 10.736 and so on. So on, so on. And so what this step does here is we multiply a and zero x want eggs, Irving this, then you do X one x to x ray and sometimes awe. Then what this stuff does it is that it essentially returns the largest valley in here in absolute terms. Yeah, and so would print out the results. So first thing that would print out is the multiplication together, and we'll print out in your second. So just be careful when I wanna print out that I printed out the transpose not be better. So you'll get a one by two vector instead of two by two. Victor. The reason why because just by the sanitation is a lot easier to read, so what we'll see is x zero is negative. 1.9 and a times by x zero is negative 1.9 and negative 1.4 large entreating next, 1.9 and so on. So on, so on and finally x for a times x four is negative. Zero point negative 0.0.4012 on negative 0.3008 with life's entry being negative. 04012

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