Chapter 2 – Vector Spaces

Once we write vectors in 3-space as (x1, x2, x3), it is not hard to generalize and write “vectors” in “27-space” as (x1, x2,… x27). The first question is: Why would you want to do this? The historical answer is quite straight forward. It helps us find answers to problems we need to solve. Most real-life problems have many more variables than just two or three. If there happen to be 27 variables, then it is useful to work in “27-space.” Fortunately much of the geometry of 2-and 3-space generalizes to “n-space,” and this helps us with problem solving considerably