Let A = 1 1 2 1 and B = 2 1 1 3 (a) Calculate Ab1 and Ab2. (b) Calculate a1B and a2B. (c) Multiply AB and verify that its column vectors are the vectors in part (a) and its row vectors are the vectors in part (b).

Calc III Lec Day 6 9/12/16 Ch. 12.1 Vector-Valued Functions and Curves in Space: Definitions and Examples 1. Vector-valued functions consist of a domain and a rule a. Domain: a collection of numbers for which the functions are valid b. Rule: Combination of functions and transformations that assign each number in the domain one and only one vector c. Are described by i. d. Range: the collection of all vectors assigned by a vector- value function to its domain e. Real-valued function: a function whose domain and range are sets of real numbers i. Every vector valued function corresponds to multiple (for this class, 3) real-valu