Fjolvar said:Hello, I'm stuck on a simultaneous eqns problem. From what I can see it seems the easiest way would be to get the matrix into row echelon form, but I'm not sure if another way would be better. I can see a pattern here but not sure what it means. I attached the problem to the page. Any help would be greatly appreciated.
Fjolvar said:Interesting, how would I use this to solve for the variables X1, X2, X3.. etc?
Linear simultaneous equations are a system of equations where each equation is linear, meaning it can be written in the form of y = mx + b. These equations have multiple variables and are solved simultaneously to find the values of the variables that satisfy all of the equations.
Gauss elimination is a method used to solve linear simultaneous equations. It involves manipulating the equations by adding or subtracting them to eliminate variables and create a system of equations with only one variable. This allows for the solution of each variable to be found.
Gauss elimination works by performing row operations on a matrix representation of the system of equations. These operations include multiplying a row by a number, adding a multiple of one row to another, and swapping rows. The goal is to reduce the matrix to a triangular form, making it easier to solve for the variables.
The purpose of solving linear simultaneous equations is to find the values of the variables that satisfy all of the equations in the system. This allows for the solution of real-world problems involving multiple variables, such as finding the intersection point of two lines or determining the optimal solution to a system of linear equations.
Linear simultaneous equations have many applications in fields such as engineering, physics, economics, and statistics. Some examples include analyzing electrical circuits, modeling chemical reactions, optimizing production processes, and predicting economic trends.