Answer: (lambda-2)(lambda-3).
- A (lambda-2)(lambda-3)
- B lambda2+5lambda+6
- C lambda2-5lambda-6
- D 2lambda2-3
Correct answer: A. (lambda-2)(lambda-3)
Explanation: Characteristic polynomial: det(λI − A) = det[[λ−2, −1],[0, λ−3]] = (λ−2)(λ−3) − 0 = (λ−2)(λ−3). This is an upper triangular matrix, so eigenvalues are the diagonal entries 2 and 3. Answer: (λ−2)(λ−3).
Concept context
Evaluation of determinants, cofactors, adjoint, inverse of matrix, Cramer's rule and area applications. Always in board and JEE.