Question

A 3x3 matrix with real entries can have:__________.

Answer 1

Answer:

a) three eigenvalues, all of them real.

d) one real eigenvalue and two complex eigenvalues.

Step-by-step explanation:

A  3x3 matrix with real entries can have : (a) three eigenvalues, all of them are real and (d) one real eigenvalue and two complex eigenvalues.

Let consider the equation for a  3x3 matrix with real entries :

$\lambda^3+a\lambda^2+b \lambda +c = 0$

From above ; we will notice that the polynomial is of 3°; as such there will be three eigenvalues in which all of them real.

Also ; complex values shows in pairs, a  3x3 matrix cannot have a three complex eigenvalues but one real eigenvalue and two complex eigenvalues.