Difference between revisions of "Linear equations"
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*[[coefficient matrix]] | *[[coefficient matrix]] | ||
*[[augmented matrix]] | *[[augmented matrix]] | ||
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| + | The basic approach for solving a matrix for the variables is [[Gaussian elimination]]. A linear system may have a unique solution, and infinite number of solution, or an inconsistency. It may also have unique solutions for some variables amid "free variables" that can take on any value. | ||
Basic theorems relating to linear equations include: | Basic theorems relating to linear equations include: | ||
Revision as of 16:29, February 21, 2010
Linear equations', or "linear systems," are sums of variables, each multiplied by a coefficient, which may be set equal to a constant. Examples of non-linear equations are polynomials and trigonometric functions.
Linear equations are represented by matrices in two ways:
The basic approach for solving a matrix for the variables is Gaussian elimination. A linear system may have a unique solution, and infinite number of solution, or an inconsistency. It may also have unique solutions for some variables amid "free variables" that can take on any value.
Basic theorems relating to linear equations include:
- there is a unique solution to a linear system of n equations in n variables if and only if the rank of the coefficient matrix is n.
