The characteristic polynomial of a 5 × 5 matrix is given below. Find the eigenvalues and their multiplicities.
-$$\lambda ^ { 5 } + 17 \lambda ^ { 4 } + 72 \lambda ^ { 3 }$$
A) 0 (multiplicity 1), 8 (multiplicity 1), 9 (multiplicity 1)
B) 0 (multiplicity $1 ), - 9$ (multiplicity $1 ), - 8$ (multiplicity 1 )
C) 0 (multiplicity 3), 8 (multiplicity 1), 9 (multiplicity 1)
D) 0 (multiplicity 3), $- 9$ (multiplicity $1 ), - 8$ (multiplicity 1 )

Question

Quizplus · Accepted Answer

The characteristic polynomial can be factored as $\lambda^3(\lambda + 9)(\lambda + 8)$, indicating eigenvalues 0 (multiplicity 3), -9 (multiplicity 1), and -8 (multiplicity 1).

The Characteristic Polynomial of a 5 × 5 Matrix Is λ5+17λ4+72λ3\lambda ^ { 5 } + 17 \lambda ^ { 4 } + 72 \lambda ^ { 3 }λ5+17λ4+72λ3

The Characteristic Polynomial of a 5 × 5 Matrix Is $\lambda ^ { 5 } + 17 \lambda ^ { 4 } + 72 \lambda ^ { 3 }$