The Characteristic Polynomial of a 5 × 5 Matrix Is $\lambda ^ { 5 } - 24 \lambda ^ { 4 } + 189 \lambda ^ { 3 } - 486 \lambda ^ { 2 }$

question 4

Multiple Choice

The characteristic polynomial of a 5 × 5 matrix is given below. Find the eigenvalues and their multiplicities.
- $\lambda ^ { 5 } - 24 \lambda ^ { 4 } + 189 \lambda ^ { 3 } - 486 \lambda ^ { 2 }$

• A) 0 (multiplicity 2), 9 (multiplicity 2), 6 (multiplicity 1 )
• B) 0 (multiplicity 2), \(- 9\) (multiplicity 2), -6 (multiplicity 1)
• C) 0 (multiplicity 2), \(- 9\) (multiplicity 2), 6 (multiplicity 1 )
• D) 0 (multiplicity 1), 9 (multiplicity \(3 ), 6\) (multiplicity 1 )