Solution to a Linear System
Solution to a Linear System:
Gaussian Elimaination and Gauss-Jordan Reduction:
Given the system AX = B to solve this system by Gaussian alimination method we transform the argumented matrix [A|B] to the matrix [C|D] which is row echelon matrix by using elementry row operations. Then to find the solutions of the system from the corresponding argumented matrix [C|D] we back substitute.
Example- Sove the system
Solution: The corresponding matrix [A|B]of the system is
By elementry row operations We transform the matrix to a row echelon matrix [C|D].
Using back substitution we now obtain
Example- Solve the system
The corresponding argumented matrix is
Hence the solution is