Very Simple Eigenvalue Calculation Need explanation please

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bmb2009
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Homework Statement



Calculate the eigenvalues of the matrix
5 2
-3 0



Homework Equations





The Attempt at a Solution



Ok we were taught that eigenvalues were calculated by taking the determinant( A - λI) = 0. So just subtract a "λ" value from the diagnol entries of the given matrix... so why aren't the eigenvalues 5 and 0? Please help me understand why the e values are 2 and 3?
 
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bmb2009 said:

Homework Statement



Calculate the eigenvalues of the matrix
5 2
-3 0



Homework Equations





The Attempt at a Solution



Ok we were taught that eigenvalues were calculated by taking the determinant( A - λI) = 0. So just subtract a "λ" value from the diagnol entries of the given matrix... so why aren't the eigenvalues 5 and 0? Please help me understand why the e values are 2 and 3?

What is the determinant of the matrix A - λI? What is the equation you get when you set this determinant to zero?

Besides: see what you get when you try to solve the equation Ax = 5x; that will tell you why 5 is not an eigenvalue.
 
bmb2009 said:
Ok we were taught that eigenvalues were calculated by taking the determinant( A - λI) = 0. So just subtract a "λ" value from the diagnol entries of the given matrix... so why aren't the eigenvalues 5 and 0? Please help me understand why the e values are 2 and 3?
I have to ask: Why do you think the eigenvalues would be 5 and 0?
 
I just realized that I butchered my algebra and now see that det(A- xI) = 0

(5-x)(-x) - (-6) = x^2 -5x + 6 = 0
(x-2) (x-3) = 0
x=2,3

Thanks for reminding me though appreciate it!