1 3 Consider the matrix A = 3 1 -2 1. Why is the matrix A orthogonally diagonalizable? 2. Find all the eigenvalues of A and determine the multiplicity of each. 3. For each eigenvalue of A of multiplicity 1, find an eigenvector of length 1. 4. For each eigenvalue of A of multiplicity k > 1 , find a set of k linearly independent eigenvectors. If this set of not orthonormal, apply Gram-Schmidt orthonormalization process to get an orthonormal set of eigenvectors. 5. Parts 3 and 4 give us an orthonormal set of n eigenvectors. Use these eigenvectors to form the matrix P. 6. Calculate the inverse of P. 7. Find the matrix P-' AP

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