Are There Integer Eigenvalues for a Specific Matrix?

[cscott]

Homework Statement

I need the eigenvalues of [[3, -1][-1, 1]] (ie [[row1][row2]])

The Attempt at a Solution

A-xI = [[3-x, -1][-1, 1-x]]

so I get the characteristic polynomial x^2-4x+2=0 from det(A-xI)=0

Is this correct? Because I won't get integer eigenvalues from it

 

[Mindscrape]

Yeah, it is right.

 

[cscott]

Won't that be really messy to bring the matrix A-xI to RREF? (with x non-integer)

 

[genneth]

But in general, there is no reason why things have to be integer...

 

[cscott]

Thanks