[Linear_Algebra] 3 types of Linear system equations

Today, we are going to discuss the three types of Linear System Equations (LSE). When the number of unknowns is equal to the number of equations, it is called a Square System. 

We can represent it as: A(n×n) X = b 

In this system, the solution is usually unique, but exceptions can exist. 

 

If the number of unknowns is greater than the number of equations, it is called an Under-constrained System.

We can represent it as: Amxn X = b (m: number of equations, n : number of unknown parameters, m < n)

In this system, there are usually infinitely many solutions. 

 

If the number of unknowns is fewer than the number of equations, it is called an Over-constrained System.

We can represent it as: Amxn X = b (m: number of equations, n : number of unknown parameters, m > n)

In this system, there is usually no exact solution. For example, consider straight lines. Two lines usually intersect at one point (if they are not parallel). However, three lines intersecting at the same common point is quite unusual.