Analyzing the consistency of a linear system based on the row [0 0 0 5 0] in echelon form

If one row in an echelon form of an augmented matrix is [0 0 0 5 0], the the associated linear system is inconsistent

To determine if the associated linear system is consistent or inconsistent based on the row [0 0 0 5 0] in the echelon form of the augmented matrix, we need to analyze the row further

To determine if the associated linear system is consistent or inconsistent based on the row [0 0 0 5 0] in the echelon form of the augmented matrix, we need to analyze the row further.

The row [0 0 0 5 0] implies the equation 0x + 0y + 0z + 5w = 0.
Simplifying this equation, we get 5w = 0.

This equation implies that 5w must equal 0 for the system to be consistent. However, since w can be any real number, there isn’t a specific value for w that satisfies the equation. Therefore, the system is inconsistent.

In summary, the associated linear system is inconsistent due to the equation 0x + 0y + 0z + 5w = 0, which has no solution.

More Answers:

Solving Systems of Linear Equations using the Row Reduction Algorithm: A Step-by-Step Guide
Understanding Basic and Free Variables in Linear Systems: Explained with Examples
A Step-by-Step Guide to Finding a Parametric Description of the Solution Set of a Linear System

Cannot search an empty string. A search keyword is required.
in echelon form" per_page="1" player_title="0" player_description="0"]

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »