1 Geometric interpretation of linear equations the kind of t

1.   Geometric interpretation of linear equations the kind of topic where you can talk about its history, who was involved in its discovery, and how it has changed over time since its initial discovery (or formulation). Be sure to include a list of your sources (in APA format if possible).please make sure it is in a 200 to 500 words so i could understand.

Solution

The history of geometric interpretation first starts with solving the system of equations using Cramer rule which came into existence in 18th century. It was named after Gabriel Cramer who published the rule for an arbitrary number of unknowns in 1750. Cramer\'s rule has a geometric interpretation that can be considered also a proof or simply giving insight about its geometric nature. These geometric arguments work in general and not only in the case of two equations with two unknowns presented here.
For a system involving two variables (x and y), each linear equation determines a line on the xy-plane. Because a solution to a linear system must satisfy all of the equations, the solution set is the intersection of these lines, and is hence either a line, a single point, or theempty set. For three variables, each linear equation determines a plane in three-dimensional space, and the solution set is the intersection of these planes. Thus the solution set may be a plane, a line, a single point, or the empty set. For example, as three parallel planes do not have a common point, the solution set of their equations is empty; the solution set of the equations of three planes intersecting at a point is single point; if three planes pass through two points, their equations have at least two common solutions; in fact the solution set is infinite and consists in all the line passing through these points.[2] For n variables, each linear equation determines a hyperplane in n-dimensional space. The solution set is the intersection of these hyperplanes, which may be a flat of any dimension.