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Example:Solve System of Equations using Matrix Method

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Explanation:

 

System of linear equations

 

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

is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by

since it makes all three equations valid.

 

General form

A general system of m linear equations with n unknowns can be written as

Here  are the unknowns,  are the coefficients of the system, and  are the constant terms.

 

Matrix equation

The vector equation is equivalent to a matrix equation of the form

where A is an m×n matrix, X is a column vector with n entries, and b is a column vector with m entries.

The number of vectors in a basis for the span is now expressed as the rank of the matrix.

(Our solved example in mathguru.com uses this concept)

 

http://en.wikipedia.org/wiki/System_of_linear_equations#Other_methods

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.