Show steps

(5) (6 Points total) Suppose that a square matrix C has a characteristic polynomial equal to (x - 1) (2 + 2) 3 (x - 3) 5. (a) (1 Point) What are the dimensions of C? Answer: (b) (1 Point ) What are the eigenvalue(s) of C? Answer(s): (c) (2 Points) What are the algebraic multiplicities (or multiplicities as our text defined) of the eigenvalues of C? (If we cannot determine the multiplicity of a particular eigenvalue, write a statement explaining why we cannot determine the multiplicities from the information given.) (d) (2 Points) What are the geometric multiplicities of the eigenvalues of C? (If we cannot determine the multiplicity of a particular eigenvalue, write a state- ment explaining why we cannot determine the multiplicities from the information given. For your information, the geometric multiplicity of an eigenvalue A of C is the dimension of the eigenspace of C corresponding to A, written dim(Ex (C)).)