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Linear Algebra

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Eigenvalues of the Sum of Matrices

LINALG-FA0ZKQ

Suppose that $A$ and $B$ are both $n\times n$ matrices. Suppose that $\lambda $ is an eigenvector of $A$ and $\mu$ is an eigenvector of $B$. Which of the following is true?

A

$\lambda +\mu$ must be an eigenvalue of $A+B$.

B

$\lambda +\mu$ may or may not be an eigenvalue of $A+B$.

C

$\lambda+\mu$ is never an eigenvalue of $A+B$.