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Linear Equations

14 November, 2016 (14:33) | General | By: admin

Solving systems of linear equations as before remains difficult for many pupils and students from other schools. But this task is very often faced with the task as a direct solve the system of equations, and other tasks as a result of decisions that arise solution of linear equations. How to quickly deal with this problem? There are lots of different methods, both direct and iterative. But the most widely used are as follows: Gauss, the method of Cramer, the matrix method. Quickly solve the system of linear equations by Gauss, please visit All you have to need to do is simply enter the original data, and the program will give a detailed solution. The method is step by step elimination of unknowns from the equations, until we arrive at an equation with one unknown. For example, what would find a solution to the joint system of three equations with three unknowns must subtract the first equation from the other so that the variable X1 deleted.

The result is one equation with three unknowns and two equation with two. Next, subtract the second equation from the third way that would eliminate the variable X2. As a result, got the third equation in one unknown X3. Further, we find X3; and substitute into the second equation, whence X2, substitute in the first and we find X1. In order that would solve the system of equations by Cramer's rule, we must find the main determinant of the matrix formed from the coefficients at Xk, where Xk is a variable. After that, we find determinants of the matrices for each variable, which are obtained by replacing the main column of the matrix corresponding to the desired variable, the column of free terms. The solution will be the ratio of the determinant of the corresponding variable to the main matrix. Like the two previous methods to solve the system of equations by matrix method is possible on site solution by this method reduces to solving the matrix equation AX = B, where A is the matrix composed of the coefficients of Xk, X a column vector Xk, B-column vector of constant terms.