Problem 3 Based on Consistency in Equation

TL;DR

Consistency of a linear equation can be determined by comparing the rank of the coefficient matrix and the augmented matrix. If they are equal, the system is consistent; otherwise, it is inconsistent.

Transcript

hi everyone today we are going to discuss problem number three based on consistency in equation you know that what is a consistent equation and what is a inconsistent equation means if your equation has a consistency or your matrix has a consistency or your system has a consistency then it has a solution otherwise it is inconsistent okay means mean... Read More

Key Insights

• 😜 Consistency in linear equations is determined by comparing the ranks of the coefficient matrix and the augmented matrix.
• 😜 If the ranks are equal, the system is consistent and has a solution.
• 😜 If the ranks are not equal, the system is inconsistent and has no solution.
• 😜 If the rank is less than the number of unknowns, the system has infinite solutions.

Questions & Answers

Q: What is the definition of a consistent equation?

A consistent equation is one that has a solution. It means that the rank of the coefficient matrix is equal to the rank of the augmented matrix.

Q: How do you determine the consistency of a system of equations?

To determine the consistency of a system of equations, compare the rank of the coefficient matrix and the augmented matrix. If they are equal, the system is consistent; otherwise, it is inconsistent.

Q: What does it mean if a system has no solution?

If the rank of the coefficient matrix is not equal to the rank of the augmented matrix, the system has no solution. This indicates that the system is inconsistent and cannot be solved.

Q: What is the minimum condition for consistency in an equation?

The minimum condition for consistency is that the rank of the coefficient matrix should be equal to the rank of the augmented matrix. If it is less than the number of unknowns, the system has infinite solutions; otherwise, it has a unique solution.

Summary & Key Takeaways

• The content discusses the concept of consistency in linear equations and matrices.

• It provides steps to determine the consistency of a system of linear equations using matrix operations.

• A specific example of a non-homogeneous system of equations is given, and the consistency is analyzed step by step.