Mechanics using linear algebra helpa please.

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The discussion revolves around finding the determinant of a 3x3 matrix and subsequently determining its eigenvalues and eigenvectors. The user initially struggles with the polynomial -lambda^3 + 6lambda^2 - 10lambda + 4 = 0, unsure about its factorization and the nature of its roots. A helpful response reveals that lambda = 2 is indeed a factor, confirming that all three roots are real. The user expresses gratitude and plans to use long division to find the remaining roots. This exchange highlights the collaborative nature of problem-solving in linear algebra.
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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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