Ppt on Non - Homogeneous Linear System

3. Types of Linear System
A) Non - homogeneous linear system : A linear system is said to be non homogeneous linear system if
AX=B where B is non zero matrix .
For e.g.
1) 5x + 7y = 352)
2x - 3y = 6
B) Homogeneous Linear System : A linear system is said to be homogeneous linear system if AX=B
where B is Zero matrix or null matrix .
For e.g.
1) 4x - 5y = 0
2) 8x + 3y = 0

4. Augmented Matrix
An augmented matri is a matrix formed by combining the columns of two matrices to form a new matrix.
The augmented matrix is an important tool in matrices used to solve simple linear equations. The number
of rows in the augmented matrix is equal to the number of variables in the linear equation.

5. Types of Non homogeneous linear system
1. Consistent System
The system is consistent if p(A) = p(A|B)
A) if p(A) = p(A|B) = No. of Variables then system has unique solutions.
B) if p(A) = p(A|B) < No. of Variables then system has infinite solutions.
2. Inconsistent System
The system is inconsistent if p(A) ≠ p(A|B) and it has no solution.

6. Key points of Non - Homogeneous systems
A non homogeneous system has no solutions if lines are parallel or does not
intersect.
A non homogeneous system has one solution if two lines intersect each other.
A non homogeneous system has infinite solution if two lines are overlapping
each other.

7. Example of Non Homogeneous Linear
System
1) x-y+2z = 2, 2x+y+4z =7, 4x-y+z=4

9. 2) 2x + 2 y + z = 5, x - y + z = 1, 3x + y + 2z = 4

11. 3) x+y+z = 3 , x+2y+3z = 4 , x+4y+9z = 6
2z = 0
x = 2, y = 1, z = 0

12. Non - homogeneous linear system contains constant term, unique solution, linear
combination and matrix operations.
These can be used in engineering, physics, economics, computer science and etc.