ABSTRACT
In this section we want to introduce the general notion of a vector space. To motivate the definition, let us recall what we did in the previous sections. On the one hand, we introduced the geometric concept of a vector as an equivalence class of arrows in space and equipped the set V of all vectors with two operations called addition and scalar multiplication. Using these operations, we could rewrite certain geometrical problems as vector equations; for example, finding the intersection of a line and a plane is equivalent to solving an equation () a + r u = b + s v + t w https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136547/a57ae1f0-6f59-46bd-bbdd-35a521b486a1/content/eq278.tif"/>
