Very Simple Eigenvalue Calculation Need explanation please

[bmb2009]

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?

 

[Ray Vickson]

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.

 

[vela]

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?

 

[bmb2009]

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!