Matrix in Linear Algebra..
 

In mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied. Matrices are used to describe linear equations, keep track of the coefficients of linear transformations and to record data that depend on multiple parameters. Matrices are described by the field of matrix theory. They can be added, multiplied, and decomposed in various ways, which also makes them a key concept in the field of linear algebra.
Mathematical definition:

An http://upload.wikimedia.org/math/a/c...19e2c58f5a.png matrix http://upload.wikimedia.org/math/3/4...a26d351ff2.png is a function http://upload.wikimedia.org/math/3/c...373667bc3e.png where http://upload.wikimedia.org/math/7/f...67759b08dd.png is any non-empty set. http://upload.wikimedia.org/math/9/7...3bdd57bc01.png is the Cartesian product of sets http://upload.wikimedia.org/math/5/7...2f3ae90629.png and http://upload.wikimedia.org/math/4/9...35d99d5a39.png
We say that matrix http://upload.wikimedia.org/math/9/2...d62f44f4ee.png is a matrix over the set http://upload.wikimedia.org/math/a/4...8be7239ede.png. Important thing to note is that, if we want to have matrix algebra, the set http://upload.wikimedia.org/math/7/f...67759b08dd.png must be a ring and matrix http://upload.wikimedia.org/math/9/2...d62f44f4ee.png must be a square matrix (see Square matrices and related definitions below for further explanation). Since the set of all square matrices over a ring is also a ring, matrix algebra is usually called matrix ring.
Since this article mainly considers matrices over real numbers, matrices shown here are actually functions http://upload.wikimedia.org/math/f/1...e83f44649e.png


For Example
The matrix
http://upload.wikimedia.org/math/6/1...06ee75372f.png or http://upload.wikimedia.org/math/4/7...9116ce109c.png is a http://upload.wikimedia.org/math/2/0...985dcb886c.png matrix. The element a2,3 or http://upload.wikimedia.org/math/2/0...e791f5997c.png is 7. In terms of the mathematical definition given above, this matrix is a function http://upload.wikimedia.org/math/9/a...3d3292725d.png and, for example, http://upload.wikimedia.org/math/f/b...aae1b44154.png and http://upload.wikimedia.org/math/c/5...4b8dd16c95.png
The matrix
http://upload.wikimedia.org/math/7/4...09e6646f63.png is a http://upload.wikimedia.org/math/e/5...a957d6443f.png matrix, or 9-element row vector.




Square matrices:

A square matrix is a matrix which has the same number of rows and columns.
http://upload.wikimedia.org/math/6/e...128c3b9842.png

Re: Matrix in Linear Algebra..
 

matrix like we study in Matric or FSc(Preengeniering)if u DONE:awub: