Question: Given a 3 x 3 matrix A with eigenvalues 1, 2, 3, and corresponding eigenvectors v1 ,v2 and v3. Which of the following is correct?

Given a 3 x 3 matrix A with eigenvalues 1, 2, 3, and corresponding eigenvectors v1 ,v2 and v3. Which of the following is correct? (1 mark} v1, v2 and v3 are eigenvectors of A2 with corresponding eigenvalues 2, 4, 6. v1, 2v: and 3V3 are eigenvectors of A2 with corresponding eigenvalues 1,4, 9. A2 has eigenvalues 1, 4, 9 but we do not know its eigenvectors. There are not enough information to determine the eigenvalues and eigenvectors of A2. None of the above

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