Java Programming Lab Code

Solving linear equation by matrix inverse method is difficult when a system has more than 3 equations and 3 unknown variables. hence, Gaussian elimination is preferred for solving system of linear equations, which has N linear equations and N unknown variables. Gaussian elimination is performed by two steps. they, upper triangular matrix back substitution System of Linear Equation by Gaussian Elimination - algorithm Given - system of Linear equations represents it in matrix form -: A - coefficient matrix X - unknown vector b - non-homogeneous vector form augmented matrix, A|b convert augmented matrix, A|b into upper triangular matrix, U by row operation U = A|b ...

A system of Linear equations AX=b is to transformed into lower triangular matrix by elementary row operation in order to find a solution vector for the unknown vector X. The lower triangulation, which is a intermediate step for solving linear equations, is explained how to finds it from the system of linear equations by row operation . Lower triangular matrix - the matrix contains all elements above the main diagonal elements are zeros. system of Linear equations Matrix representation of system of Linear equations Low Triangular matrix algorithm steps Given matrix A, b and A is 3x3 and b is 3x1 matrix Augmented Matrix mat = A | b maxpivot - finds m th row has maximum value (pivotal value) along c th column RowOperation-swap - swaping two rows c th and m th RowOperation-add - Rc2 th <- ratio R c + R c2 For c=mat.Nrow-1 to ...

It explains how to decompose an augmented matrix into upper triangular matrix by row operation and it is implemented in Java programming. A system of linear equation is represented in matrix format by a matrix called A and two column vectors called X and b respectively. AX =b The X is an unknown vector and is to be found as solution for a system of linear equations. The Gaussian elimination is one of the methods for finding the unknown vector of a linear system of equations. The Gaussian elimination has two main steps Augmented matrix into Upper Triangular Back substitution Here, it contains explanation about how to decompose an augmented matrix into upper triangular matrix. The augmented matrix consist of coefficient matrix A and a column vector b i.e. Alb and it is decomposed into upper triangular matrix by elementary row operation. A matrix has rows and columns arrangements of elements and if all elements below th...