Linear System Of Equations

Linear System of Equations

A linear system of equations is a set of linear equations in variables (sometimes called "unknowns"). Linear syste represented in matrix form as the matrix equation

where

is the matrix of coefficients, is the column vector of variables, and

is the column vector of solutions.

If

, then the system is (in general) overdetermined and there is no solution.

If

and the matrix

is nonsingular, then the system has a unique solution in the variables. In particular, as sh

rule, there is a unique solution if

has a matrix inverse

If , then the solution is simply less than or the empty set.

. If

. In this case,

has no matrix inverse, then the solution set is the translate of a subs

If two equations are multiples of each other, solutions are of the form

for a real number. More generally, if , then the system is underdetermined. In this case, elementary matrix op used to solve the system as far as possible, then the first components can be solved in terms of the last com solution space.

SEE ALSO: Cramer's Rule, Determinant, Linear Equation, Matrix, Matrix Equation, Matrix Inverse, Null Space, Simul

System of Equations. [Pages Linking Here]

REFERENCES: Calc101.com. "Step-by-Step Linear Equations, Matrices and Determinants."

http://calc101.com/webMathematica/matrix

LAST MODIFIED: December 8, 2002 CITE THIS AS:

Weisstein, Eric W. "Linear System of Equations." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LinearSystem

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