- #1
Treadstone 71
- 275
- 0
"Let T be a the transformation on V = C^3 given by the equation
T(x)=-y-2z
T(y)=3x+5y+7z
T(z)=-2x-3y-4z
where (x,y,z) denotes the standard basis. Find the eigenvalues of T and the corresponding eigenspaces."
Is there a way to find the eigenvalues without solving the 3 equations? How do I find the characteristic polynomial of T without resorting to anything related to determinants?
T(x)=-y-2z
T(y)=3x+5y+7z
T(z)=-2x-3y-4z
where (x,y,z) denotes the standard basis. Find the eigenvalues of T and the corresponding eigenspaces."
Is there a way to find the eigenvalues without solving the 3 equations? How do I find the characteristic polynomial of T without resorting to anything related to determinants?