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Example:Solve System of Equations using Matrix Method

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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)




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.