How to check consistency and inconsistency of the system of linear equations

"Welcome to Math4You! In this video, we'll be exploring How to check consistency and inconsistency of system of linear equationsa fundamental concept in linear agebra.

What is system of linear equation ?
What is consistence system ?
Under what condition a system will be consistence ?
Under what condition will be inconsistence?

In this video, we'll cover How to check consistency and inconsistency of system of linear equations to help you understand Key Concept. Whether you're a student, teacher, or simply curious about system of linear equations , this video is designed to help you learn and grow.

Timestamps :
System of linear equatins : 0:35
Dependent system : 2:20
Inconsistence system of linear equation: 2:54
Independent system of linear equation:3:15
Examples: 5:00

Consistency and inconsistency:

A consistent system of linear equations has:
Characteristics
One unique solution (intersection point)
Infinitely many solutions (dependent equations)

Examples
Unique Solution*
2x + 3y = 7
x - 2y = -3

Infinitely Many Solutions*
2x + 2y = 4
4x + 4y = 8 (dependent equations)

Properties
Consistent systems have either one or infinitely many solutions.
Inconsistent systems have no solutions.

Additional resources:

   • Arithmetic sequence with solved examples  
   • The Power Rule For Derivatives  
   • Find angle x, 2x and 6x in the given ...  
   • How to find ? in the given Mathematic...  

   • How to find ? in the given figure usi...  
   • Applications of straight angle and ve...  

   • Straight angle | Find the value of an...  

   • Problem on vertical angles| Find valu...  

   • Limit_(x tend to zero)(1-sinx/cos^2x)  

Don't forget to like, comment, and subscribe for more educational content. Practice what you've learned or explore related topics