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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 :
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.