Upgrade to access all content for this subject

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

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

The matrix must be singular.

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

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

The matrix must be invertible.

None of the above.