A Study On Linear Equations, Solutions Of Linear Equations

This Paper is the study of a system of linear equations in n unknowns and finding solution by various methods, Gauss elimination method, Gauss Jordan method, Gauss Seidel method. A System of Linear Equations is two or more linear equations together. The solution to a system of linear equations is the point at which the lines representing the linear equations intersect. When there is no solution then the system of linear equations is referred as "inconsistent”. If there is one or infinitely many solutions then the system of linear equations is referred as “consistent". Many problems in Engineering and applied sciences require the solution of System of equations. The system of linear equations used to solve age problems, to calculate speed, distance and time of a moving object. It is also used to calculate money and percentage problems,Work, time and wages problems. Problems on force and pressure can also be solved.

Riesgo relativo, sensibilidad y especificidad: un enfoque desde el análisis matemático y el álgebra lineal / Relative risk, sensitivity, specificity: an approach from mathematical analysis and linear algebra

El riesgo relativo (RR), la razón de productos cruzados (OR), la especificidad (E) y la sensibilidad (S) constituyen medidas de resumen para variables cualitativas de interés en Medicina. Se presenta el RR como una función continua de dos variables y se analiza la condición para la cual este se aproxima a la OR a partir de su desarrollo en serie de potencias. La sensibilidad, la especificidad y los valores predictivos (VPP y VPN) se analizan como funciones continuas de una variable en todo su dominio, con un comportamiento asintótico característico. A partir del estudio de un sistema de ecuaciones lineales homogéneo se deduce una ecuación general que vincula S, E, VPP y VPN y se discuten diferentes casos de interés(AU)

The relative risk (RR), the odds ratio (OR), the specificity (E) and the sensitivity (S) are measures for qualitative variables of medical interest in Medicine. It is analysed the RR as a continue function of two variables as well as the conditions by which it is approximated to the OR by means of a power series expansion. It is analysed too the sensitivity, the specificity and the predictive values as continue functions of one variable in all its domains of definition as well as the asymptotic behaviour of these functions. It is discussed different interesting cases by means of a system of linear equations in S, E, VPP, VPN(AU)