Simultaneous Linear Elimination Method: Equations and Matrices (Part - 1)

Simultaneous Linear Elimination Method is a technique used to solve a system of linear equations. This method involves eliminating one variable at a time by adding or subtracting equations. The goal is to simplify the system until we have a single equation with one variable.

Equations and Matrices

A system of linear equations can be written in the form of Ax = b, where A is a matrix of coefficients, x is a vector of variables, and b is a vector of constants. In order to solve the system, we need to find the values of x that satisfy the equation.

The Simultaneous Linear Elimination Method involves manipulating the matrix A and the vector b to simplify the system of equations. This is done by adding or subtracting equations, which is equivalent to multiplying the matrix A by a certain factor.

Steps in the Simultaneous Linear Elimination Method

1. Write the system of equations in the form of Ax = b, where A is the matrix of coefficients, x is the vector of variables, and b is the vector of constants.

2. Choose a variable to eliminate. This is usually the variable with the smallest coefficient.

3. Multiply one or both equations by a factor so that the coefficients of the chosen variable are equal in magnitude but opposite in sign.

4. Add or subtract the equations to eliminate the chosen variable. This will result in a new equation with one fewer variable.

5. Repeat steps 2-4 until only one variable remains.

6. Solve the remaining equation to find the value of the last variable.

7. Substitute the values of the variables back into the original equations to check that they satisfy the system.

In conclusion, the Simultaneous Linear Elimination Method is a powerful technique for solving systems of linear equations. By manipulating the matrix of coefficients and the vector of constants, we can simplify the system and find the values of the variables that satisfy the equations.