Math 290 Homework 3

Math 290 Homework #3
Due date: Thursday, September 7

Section 2.1 (pp. 55--59)

#39, #40, #41, #43.
#49. The converse of a statement of the form "If P, then Q" is the statement "If Q, then P". So the second part of this problem asks you to prove that the following statement is false: "if the ith row of AB has all zero entries, then so does the ith row of A." To carry out this proof, you need to construct a pair of matrices A, B such that the ith row of AB has all zero entries, but the ith row of A does not.

Section 2.2 (pp. 69--71)

#9, #23, #24.
#37, #38. The goal, of course, is to give the right answer without having to actually calculate every single one of the matrices A², A³, ...., A¹⁹, A²⁰.
#50, #53.