Statistics Solutions

[See Solution] Let

Question: Let

\[A=\left[\begin{array}{lll} 2 & 1 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \end{array}\right]\]
  1. Derive the eigenvalues of A. Report all steps in the process. No marks will be awarded for an unsupported answer.
  2. Derive the eigenvector of unit length corresponding to the largest eigenvalue of \(\mathrm{A}\). Report all steps in the process. No marks will be awarded for an unsupported answer.
  3. Derive the eigenvector of unit length corresponding to the second largest eigenvalue of A. Report all steps in the process. No marks will be awarded for an unsupported answer.
  4. Do the eigenvectors derived in (b) and (c) form an orthonormal set of vectors? Briefly explain. No marks will be awarded for an unsupported answer.
  5. Are the eigenvectors derived in (b) and (c) linearly independent? Briefly explain. No marks will be awarded for an unsupported answer.
  6. Given the eigenvalues of \(\mathrm{A}\), what do you conclude about the rank of \(\mathrm{A}\) ? Briefly explain

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