Answer to Question #45358 in Matrix | Tensor Analysis for Michelle

Question

1. Find all values of a, b, c, and d for which A is skew-symmetric.

A = [[0, 2a-3b+c, 3a-5b+5c],[-2, 0, 5a-8b+6c],[-3, -5, d]]

2. Let R be the 5x5 matrix:

[[-8, 33, 38, 173, -30],[0, 0, -1, -4, 0],[0, 0, -5, -25, 1],[0, 0, 1, 5, 0],[4, -16, -19, -86, 15]]

(a) Using technology, and the characteristic polynomial of R and hence and the eigenvalues.

(b) For each of the eigenvalues, determine (by hand) how many linearly independent eigenvectors can be found.