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# Matrices

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### Matrices

1. 1. MATRIX<br />
2. 2. MATRICES<br />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.<br />
3. 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<br />
4. 4. SIMMETRIC MATRIX<br />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<br />
5. 5. TRASPOSE MATRIX<br />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)<br />
6. 6. TRIANGULAR MATRIX<br />Square matrix has its elemetos null above or below its main diagonal<br />
7. 7. AUGMENTED MATRIX<br />The augmented matrix of a matrix is obtained by changing a matrix in some way. <br /> Given the matrices A and B, where:<br /> Then, the augmented matrix (A|B) is written as:<br />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.<br />
8. 8. MATRIX MULTIPLICATION<br />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:<br />
9. 9. DETERMINANT<br />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. <br />( a11 ) ( a22 ) - ( a21 ) ( a12 )<br />
10. 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.<br />
11. 11. BIBLIOGRAPHY<br />Introducción al álgebra lineal Escrito por José Manuel Casteleiro Villalba <br />Álgebra lineal y sus aplicaciones Escrito por Gilbert Strang<br />http://en.wikipedia.org/wiki/Matrix_(mathematics)<br />