Applied Mathematics 1411A/B Chapter Notes - Chapter 4.1: Scalar Multiplication, Mexican Peso

• School: Western University
• Department: Applied Mathematics
• Course: Applied Mathematics 1411A/B
• Professor: Bogdan Tudose

Document Summary

In this section we will observe the basic properties of vectors in order to extend certain concepts to apply to objects in general. If v is a set of objects, then we can call v a vector space, and the objects inside vectors if the following 10 conditions are met: If u & v are objects in v, then u + v is in v u + v = v + u u + (v + w) = (u + v) + w. There is an object in v that is the zero vector so u + 0 = u & 0 + u = u. For each u in v there is a -u called the negative so -u + u = 0. If k is any scalar and u is in v, then ku is in v k(u + v) = ku + kv (k + m) u = ku + mu k(mu) = (km)(u)