System of linear equations (linear system)
is a collection of one or more linear equations involving the same variables.
A system of linear equations, also known as a linear system, is a collection of one or more equations in variables that can be expressed in the form of Ax = b, where A is a matrix of coefficients, x is a column vector of variables, and b is a column vector of constants. Each equation in the system provides a constraint that the solution must satisfy.
Linear systems can have one unique solution, infinitely many solutions, or no solution at all. A system with a unique solution means that there is exactly one set of values for each variable that satisfies all the equations in the system. A system with infinitely many solutions means that there are multiple sets of values for the variables that satisfy all the equations in the system. A system with no solution means that there is no set of values for the variables that can satisfy all the equations in the system simultaneously.
Linear systems have a wide range of applications in various fields, including engineering, physics, finance, and economics. They can be solved using various techniques such as matrix inversion, Gaussian elimination, and determinants. Linear systems are also used in linear programming to find optimal solutions to problems involving the maximization or minimization of linear objectives, subject to linear constraints.
More Answers:
Understanding the Three Types of Solutions for Systems of Linear Equations: Unique, No Solution, and Infinitely Many SolutionsUnderstanding Solution Sets: Exploring Finite and Infinite Solutions and the Empty Set.
Mastering Linear Algebra: Understanding Equivalent Linear Systems and their transformation through Row Operations