Question

Suppose a 3x3 real matrix A has only two (real) distinct eigenvalues. Suppose that trace(A) = 1 and det(A) = -45 . Find the eigenvalues of A with their algebraic multiplicities.

smaller eigenvalue = ?
has mulitiplicity = ?

larger eigenvalue = ?
has mulitiplicity = ?
.

Answer 1

recall that if the eigenvalues are u and v, then
u+v = trace(A)
uv = |A|

now git 'er done