1.4.2. Hints for Eigenvalue / Eigenvector Homework Assignment

1. 1. See the examples near the end of the Finding Eigenvalues and Eigenvectors page. Remember that the eigenvectors are the columns of the X matrix and the eigenvalues are on the diagonal of the L matrix.

   2. See the example in Finding Eigenvectors. Remember that there are two characteristic equations – one for each eigenvalue.

   3. See the example in Finding Eigenvectors. For each eigenpair, just do the multiplications \(\mathbf{A}\,\bm{x}_i\) and \(\lambda_i\,\bm{x}_i\). Verify that the products are the same for each eigenpair.

2. See Roots of a Polynomial by Eigenvalues for an example