Linear Equations in More Than Two Variables
A linear equation can involve more than two variables. The general linear equation in n variables is:
In this form, a1, a2, …, an are the coefficients, x1, x2, …, xn are the variables, and b is the constant. When dealing with three or fewer variables, it is common to replace x1 with just x, x2 with y, and x3 with z, as appropriate.
Such an equation will represent an (n–1)-dimensional hyperplane in n-dimensional Euclidean space (for example, a plane in 3-space).
In vector notation, this can be expressed as:
where is a vector normal to the plane, are the coordinates of any point on the plane, and are the coordinates of the origin of the plane.
Read more about this topic: Linear Equation
Famous quotes containing the word variables:
“Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.”
—Paul Valéry (1871–1945)