Linear algebra introduction

In the essential knowledge of a mathematician, physicist, engineer, and other scientists, there must be mathematical analysis, which is born from linear algebra. Thanks to its application in any area, it has helped us understand the reality of phenomena, both tangible and theoretical.

The fundamental approach by which the linear algebra, is how to solve a system of linear equations with n unknowns.

In linear algebra, several subjects are handled in which we find: matrices, vectors and linear equations.


As an introduction to linear algebra, we will define what a matrix is:

A matrix, be a two-dimensional or rectangular arrangement of n rows and m columns that is represented as follows:


And to each element of the matrix we will callij.

Example: Matrix A:


This matrix has n = 3 rows and m = 2 columns. Its elements will be11 = 1; to12 = 2; to21 = 3; to31 = 5; to32 = 6. It can also be said that it is a 3 × 2 matrix.

Exercise 1: Build matrix A(3 × 2). Where, its elements toij = i + j.

First, we must recognize that matrix A will have n = 3 rows and m = 2 columns:


For two matrices to be equal, you must first comply with both matrices having the same number of rows and columns, secondly, their elements one by one must be equal, that is:

A(n × m)= B(n × m)

In addition the elements:

aij = bij