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Linear equations (view source)

Revision as of 16:17, February 21, 2010

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''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''', 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.
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Linear equations are represented by matrices in two ways:
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*[[coefficient matrix]]
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*[[augmented matrix]]
    
Basic theorems relating to linear equations include:
 
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''.
 
* 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''.
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*
       
[[Category:linear algebra]]
 
[[Category:linear algebra]]
 
[[Category:mathematics]]
 
[[Category:mathematics]]
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