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:
“The variables are surprisingly few.... One can whip or be whipped; one can eat excrement or quaff urine; mouth and private part can be meet in this or that commerce. After which there is the gray of morning and the sour knowledge that things have remained fairly generally the same since man first met goat and woman.”
—George Steiner (b. 1929)