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Matrix

Definition: Is an arrangement of items into labeled rows and columns within a table. Description: A Matrix may indicate a branch of items with some kind of connection; this connection may describe a system of lineal equations, and it is really useful because it helps a lot in some cases. The Matrices have many operations, such as addition, multiplication (by a scale number, or by another Matrix), and properties, as associativity, neutral element and others. There are 2 ways to resolve a Matrix: The Gauss-Jordan Elimination and the Gaussian Elimination.

Classification: A Matrix may be classified in many ways: 1- If the Matrix has the same numbers of rows as columns, it is called squared. 2- If the Matrix has a line of zeros above its main diagonal (diagonal who comes from the top left corner and finish in the bottom right corner), it is called Upper Triangular, in the other hand if the Matrix has a line of zeros below its main diagonal, it is called Lower Triangular. 3- If the Matrix has only ones in its main diagonal it is called identity Matrix. 4- If the Matrix has numbers only in its main diagonal it is called Diagonal Matrix.

Comparison and Contrasts: As a comparison, when adding Matrices, this operation has the property of associtivity, in the same way, when multiplying by a scale number, this property shows up again. As a Contrast, when multiplying a Matrix by another, this operation doesn’t have the property of commutativity, in the case of the addiction, this property is allowed.