2. Let A be a 2 2 matrix. Assume and 2 are the two distinct non-zero...

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2. Let A be a 2 2 matrix. Assume and 2 are the two distinct non-zero eigenvalues of A. Determine whether the following statements are always true? If true, justify why. If not true, provide a couterexample. Statement A: If v is an eigenvector corresponding to and v2 is an eigenvector corresponding to 2, then v v2 is an eigenvector of A, corresponding to eigenvalue + \2. Statement B: If c R, then cv is an eigenvector of A, corresponding to \. 2. Let A be a 2 2 matrix. Assume and 2 are the two distinct non-zero eigenvalues of A. Determine whether the following statements are always true? If true, justify why. If not true, provide a couterexample. Statement A: If v is an eigenvector corresponding to and v2 is an eigenvector corresponding to 2, then v v2 is an eigenvector of A, corresponding to eigenvalue + \2. Statement B: If c R, then cv is an eigenvector of A, corresponding to \.