1. Guass-jordan Reduction :
Step 1: Form the augmented matrix corresponding to
the system of linear equations.
Step 2 : Transform the augmented matrix to the matrix
in reduced row echelon form by using
elementary row operations.
Step 3 : Solve the linear system corresponding to the
matrix in reduced row echelon form.

2. Number of Solutions of a System of Linear Equations:
For any system of linear equations, precisely one of the following is true.
The system has exactly one solution.
The system has an infinite number of solutions.
The system has no solution.

3. Exercise : 2.3 Page # 113 Qn # 5 (b)
Find all solutions, if any exist, by using the Gauss Jordan reduction method.
Step 1 : Augmented matrix for the set is:

4. The given system has exactly one solution.
Step 2 : The matrix in reduced row echelon form is
Step 3 : The Solution is
The given system has exactly one solution.

5. Exercise 2.2, Page #114,Qn #7(c)
Solve the linear system, with given augmented matrix, if it is consistent.
Step 1 :
Step 2 : The matrix in reduced row echelon form is

6. Step 3 : The linear system corresponding to the
matrix in reduced row echelon form is
The solution are
The given system has infinitely many solutions.

7. Example Solve for the following system
Step 1 : The augmented matrix is

8. Step 3 : The matrix in reduced row echelon
form is
Step 3 : The linear system corresponding to the
matrix in reduced row echelon form is
since , there is no solution.