Day04HWsoln - Exercise Set 3 Solutions In this homework set...

Exercise Set 3 Solutions
In this homework set, we will practice finding eigenvalues and eigenvectors
when the eigenvalues are either complex or the matrix is defective.
1. Given a 2 × 2 defective matrix A with double eigenvalue λ , eigenvector
v and generalized eigenvector w , show that the function:
e
λt
( t v + w )
solves the differential equation x 0 = A x .
2. Exercises 1, 3, pg. 409 (Section 7.6, solve with complex evals/evecs)
Solutions in the text.
3. Exercises 1, 3, 7, pg. 429 (Section 7.8, solve with degenerate matrix)
Solutions in the text.