Mechanics using linear algebra helpa please.

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SUMMARY

The discussion centers on finding the determinant of a 3x3 matrix and subsequently determining its eigenvalues and eigenvectors. The polynomial derived from the determinant is -λ³ + 6λ² - 10λ + 4 = 0. A participant confirms that λ = 2 is a factor, indicating that all three roots of the polynomial are real. The conversation concludes with the user expressing gratitude for assistance in recalling the long division method necessary to find the remaining roots.

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  • Understanding of 3x3 matrix operations
  • Knowledge of determinants and their properties
  • Familiarity with eigenvalues and eigenvectors
  • Ability to perform polynomial long division
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  • Study methods for calculating determinants of matrices
  • Learn how to find eigenvalues and eigenvectors of matrices
  • Explore polynomial factorization techniques
  • Review polynomial long division for solving cubic equations
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Students and educators in linear algebra, mathematicians working with matrix theory, and anyone seeking to deepen their understanding of eigenvalue problems and polynomial equations.

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Question 20. The 3 equations I am using were given to me by my prof, so I can't imagine it being wrong. But you never know. Well as you can see my work is shown. My goal is to find the determinant of this 3 x 3 matrix, and from the determinant find the eigenvalues. Then using those eigenvalues to find the eigenvectors.The problem I run into when doing the determinant and then setting it equal 0 I get: -lamda^3 + 6lamda^2 - 10lamda + 4 = 0. Which I can't really see how to factor. So I can't imagine it having all real roots. And I am pretty sure it should have all real roots.

Thanks for any help.

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lambda = 2 is a factor and all three roots are real.
 
Oh my gosh, you are the best. So now all I got to do is remember how to do long division to get the other 2 roots :). Thx again.
 

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