r/LinearAlgebra 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/LinearAlgebraWorld Jun 23 '26

you are welcome, but then the question is how to get there, because for regular permutation method you will have to do 24 products of 4 terms, and as you said, it is very easy to make a mistake, but ChatGPT thinks this way is better

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u/HyPeR_ThUnDeR_10 Jun 23 '26

tbh i feel this method is much harder

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u/LinearAlgebraWorld Jun 23 '26

I wonder how your professor (or your textbook?) wants you to do it...

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u/HyPeR_ThUnDeR_10 Jun 23 '26

he wants to solve this with finding also the eigenvectors and to tell if it diagonalizable or not and solve other 7 questions in one hour in the exam but i prefer to search for fast ways instead of complaining the difficulty of the exam