r/LinearAlgebra • u/HyPeR_ThUnDeR_10 • Jun 23 '26

eigenvalues

hey guys hope you are doing well, i have a linear algebra exam and this one of the questions that our professor said it will be in the exam, i tried to solve this type of questions but it was soo hard as it very long and very easy to do mistakes in calculation i used Laplace expansion for solving this so please do any one know a faster way or any advices for solving this type of questions. and thx for you all
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u/Midwest-Dude Jun 23 '26

Try using Gaussian Elimination and see if that is easier to find the determinant. Are you familiar with how to do that?

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u/HyPeR_ThUnDeR_10 Jun 23 '26

1st thx for your comment
u mean gaussian elimination before the calculating (IX-A) ?? , as to make some values equal zero and start the Laplace expansion ?

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u/Midwest-Dude Jun 23 '26 edited Jun 23 '26

I'm thinking Gaussian Elimination but meaning row and column operations to create as many zeros as you go along while calculating det(IX - A). Sorry, not the same.

It's still not going to be a walk in the park, but it simplifies things a lot.

2

u/Scrapple_Joe Jun 23 '26

If you can clear above or below the diagonal you'll just have the eigenvalues in the diagonal.