Explore: Linear Algebraic Equations

In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example

of algebraic structures. Within certain algebraic structures, it examines the use of variables in equations and how to manipulate these equations. Algebra

includes the study of equations that involve nth roots and, more generally, algebraic expressions. This makes the term algebraic equation ambiguous outside

fewer equations than unknowns and involve finding integers that solve all equations simultaneously. Because such systems of equations define algebraic curves

phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions

is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions

Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b

A\mathbf {x} =\mathbf {0} \right\}.} The matrix equation is equivalent to a homogeneous system of linear equations: A x = 0 ⇔ a 11 x 1 + a 12 x 2 + ⋯ + a 1 n

two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true

associated plot of the equations. For other ways to solve this kind of equations, see below, System of linear equations. A quadratic equation is one which includes