et A� be an 5 by 5 matrix, let v1�1 be an eigenvector of A� with eigenvalue λ1�1 and let v2�2 be an eigenvector of A� with eigenvalue λ2�2. Select all items below that are true. A. The vector −5v1−5�1 need not be an eigenvector of A�. B. If v1�1 is a scalar multiple of v2�2, then λ1=λ2�1=�2. C. The vector −5v1−5�1 is an eigenvector of A�.
Let A� be an 5 by 5 matrix, let v1�1 be an eigenvector of A� with eigenvalue λ1�1 and let v2�2 be an eigenvector of A� with eigenvalue λ2�2. Select all items below that are true.
A. The
B. If v1�1 is a scalar multiple of v2�2, then λ1=λ2�1=�2.
C. The vector −5v1−5�1 is an eigenvector of A�.
D. For any real number c�, cλ1��1 is also an eigenvalue of A�.
E. If 0 is an eigenvalue of A�, then A� is singular.
F. If λ1=λ2�1=�2, then v1+v2�1+�2 is an eigenvector of A� (as long as it is nonzero).
G. If λ1=λ2�1=�2, then v1�1 must be a scalar multiple of v2�2 (or vice versa).
H. It is entirely possible that the zero vector is an eigenvector of A�.
I. If A� is singular, then 0 is an eigenvalue of A�.
J. None of the above
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