What are the unit eigenvectors for the matrix A = [5 -2; -2 8]?

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SUMMARY

The unit eigenvectors for the matrix A = [5 -2; -2 8] are definitively calculated as follows: for the eigenvalue λ = 4, the corresponding unit eigenvector is x1 = (-2/sqrt(5), -1/sqrt(5))^T, and for the eigenvalue λ = 9, the corresponding unit eigenvector is x2 = (1/sqrt(5), -2/sqrt(5))^T. The characteristic polynomial is derived from the determinant equation det(A - hI) = 0, leading to these eigenvalues. The calculations confirm the results are accurate and consistent.

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Homework Statement



I'm trying to find the unit eigenvectors corresponding to the following matrix

A = [5 -2; -2 8] ; means new row

Homework Equations



det(A - hI) = 0

The Attempt at a Solution



I get lambda = 4 and 9

unit eigenvector corresponding to lambda = 4

x1 = ( -2/sqrt(5), -1/sqrt(5) )^T

unit eigenvector corresponding to lambda = 9

x2 = (1/sqrt(5), -2/sqrt(5) )^T

Could someone please let me know if they get the same result. Thanks!
 
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