1. MATRIX

2. MATRICES Matrices are a keytool in liner algebra, one use of matrices istorepresentliner transformation. Matrices can also keep track of the coefficients in a system of linear equations.

3. For a square matrix, the determinant and inverse matrix (when it exists) govern the behavior of solutions to the corresponding system of linear equations

4. SIMMETRIC MATRIX It’s a squarematrixthatisequaltoitstraspose. Forthesimmetricmatrix A A(i,j)=A(j,i), then A=A(traspose) The elements of a symmetric matrix are symmetric with respect to the main diagonal

5. TRASPOSE MATRIX We find this matrix when we change the established order of rows by columns and columns by rows, as follows, with a matrix A = a (i, j) we obtain its transpose and At = a (j, i)

6. TRIANGULAR MATRIX Square matrix has its elemetos null above or below its main diagonal

7. AUGMENTED MATRIX The augmented matrix of a matrix is obtained by changing a matrix in some way. Given the matrices A and B, where: Then, the augmented matrix (A|B) is written as: This is useful when solving systems of linear equations; the augmented matrix may also be used to find the inverse of a matrix by combining it with the identity matrix.

8. MATRIX MULTIPLICATION Multiplication of two matrices is defined only if the number of columns of the left matrix is the same as the number of rows of the right matrix. If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot-product of the corresponding row of A and the corresponding column of B:

9. DETERMINANT the determinant is a special number associated with any square matrix. The fundamental geometric meaning of a determinant is a scale factor for measure when the matrix is regarded as a linear transformation. ( a11 ) ( a22 ) - ( a21 ) ( a12 )

10. Thus a 2 × 2 matrix with determinant 2 when applied to a set of points with finite area will transform those points into a set with twice the area. Determinants are important both in calculus, where they enter the substitution rule for several variables, and in multilinear algebra.

11. BIBLIOGRAPHY Introducción al álgebra lineal Escrito por José Manuel Casteleiro Villalba Álgebra lineal y sus aplicaciones Escrito por Gilbert Strang http://en.wikipedia.org/wiki/Matrix_(mathematics)