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 of quantification, ‘something,’ ‘nothing,’ ‘everything,’ range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true.”
—Willard Van Orman Quine (b. 1908)