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Let $A$ be as in Exercise 9 . Use the inverse power method with $\mathbf{x}_{0}=(1,0,0)$ to estimate the eigenvalue of $A$ near $\alpha=-1.4,$ with an accuracy to four decimal places.

an estimate for the eigenvalue to four decimal places is $-1.4244$ . The actual eigenvalue is $(7-\sqrt{97}) / 2$ or $-1.424429 .$ to six decimal places.

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 8

Iterative Estimates for Eigenvalues

Vectors

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Okay, So in this question, we want to estimate the idea value off this mattress right here using that invest help, Mrs. So once again, I've created a program in quietly and can run this yourself. So just go through This appears This is the A matrix. This is your Alfa that you said to me Mars 1.4 and we want to try this 10 times. Well, are trying sometimes. So this is what it does. So what district does when we performed the inverse power step? We want to solve a minus. Phi out for identity. Why, Kay? Is it ex k? So we want to solve. For why So instead, let's move a minus. I the inverse of the over to decide. So then we have Why, Kay, deep into a Mars, a upper agency in verse. Thanks. Okay, So this is what this that does a minus. Alpha times my identity Take the inverse of that and we multiply it by X. So then we'll we will get new, Which is the entry in Why the entry in why? Which which has the highest absolute value possible So that Mr Does and then new is it to have a plus one of a mule. Then X K is equal to that X is equal to why I ever knew So then here. So here I print out the I didn't baby value. Sorry, as in this movie the item vector. So this is for zero. The news here isn't used 1.375 then x once after the first iteration This is your again. This is your approximated. I bet that approximate it approximated I didn't value. And so it's all this house on this hole. So finally approximated Ivan. Bet that is 10.37 and negative 0.78 How approximated Aiken value is negative. 1.4244

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