- #1
karush
Gold Member
MHB
- 3,269
- 5
ok, just now looking at some examples of how to do this $x_4$ is just a row with all zeros
The purpose of using vectors is to represent the set as a line in four-dimensional space. This allows for a more efficient and accurate way of describing the set and its properties.
To describe a set as a line in R^4, you need to use four-dimensional vectors that represent the coordinates of points on the line. These vectors can be manipulated to determine the direction and length of the line.
No, vectors can only be used to describe sets that exist in four-dimensional space. If a set exists in a different number of dimensions, a different method must be used to describe it as a line.
R^4, or four-dimensional space, is used because it allows for a more comprehensive representation of the set. It also allows for more complex calculations and analysis to be performed on the set.
One limitation is that not all sets can be accurately represented as a line in four-dimensional space. Additionally, the use of vectors may not be the most efficient method for describing certain types of sets.