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Linear Algebra

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Zero Eigenvalue

LINALG-09XGBC

Suppose that a matrix $M$ has eigenvalue zero. Which of the following statements are TRUE? Select ALL that apply.

A

It is impossible that a matrix has zero as an eigenvalue.

B

The matrix must be singular.

C

The matrix must also have the zero vector as an eigenvector.

D

Zero must be a root of the characteristic polynomial of the matrix.

E

The matrix must be invertible.

F

None of the above.