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shiri

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A) lambda = −1 is an eigenvalue for A

B) The vector v is an eigenvector for A corresponding to the eigenvalue lambda = −1.

C) lambda = 0 is an eigenvalue for A

D) Any vector w perpendicular to v is an eigenvector for A corresponding to the eigenvalue lambda = −1.

E) Any vector w perpendicular to v is an eigenvector for A corresponding to the eigenvalue lambda = 0.

A) A matrix must have a non-zero eigenvalue.

B) The vector is an eigenvector of corresponding to the eigenvalue.

C) See A

D) When a vector is perpendicular to A, it must be zero for eigenvalue (If it was nonzero eigenvalue, then it is not perpendicular)

E) See D

So far I believe A, B, E are true? What do you think? Please help me.