Homework 5 - due Monday, July 28, in class

Each problem is worth 10 points.

The following problems are from the textbook:

section 5.3: #3, #14
section 6.1: #19, #33
section 6.2: #8, #10, #30
section 6.3: #4, #8

Additionally, solve the following problem:
Fix a real number lambda. Let A_n denote an n x n matrix with lambda on the main diagonal, with 1 on the diagonal immediately above the main diagonal, and with 0 everywhere else. By the definition of the exponential, find e^(A_n) for n=2 and n=3. Can you guess the result for a general n?