ENEE 498M Lecture 11 Homework 1. Find the eigenvalues and eigenvectors of { -2 -9 5 -5 -10 7 -9 -21 14 } Verify with Matlab . NOTE:

-21 12}

Are the eigenvalues orthogonal?

5.      The trace of a square matrix, denoted by tr(A)  is defined as the sum of the diagonal elements. Prove that trace(A + B) = trace(A) + trace(B)

6.      Use the above to prove that tr(A)  is equal to the sum of the eigenvalues of the matrix.