Applied Mathematics 1411A/B Chapter 4: Chapter 4 List of Theorems

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

Document Summary

If v is a set of objects, then we can call v a vector space, and the objects inside vectors if the following. 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) Let v be a vector space, u a vector in v and k a scalar, then: a) b) c) d) 0u = 0 k0 = 0 (-1)u = -u.