Traffic flow linear algebra

In this video, we study a traffic flow problem using systems of linear equations.
A network of one-way streets is given, where the directions of traffic flow are indicated by arrows and the known traffic entering or leaving the network is marked on the outer roads.

The unknown traffic flows along the internal roads are represented by
x1, x2, x3 and x4.

Using the principle of conservation of traffic, we analyze each junction of the network.
At every junction, the total traffic entering is equal to the total traffic leaving.
This idea helps us form a system of linear equations based on the given traffic directions.

The video explains:

How to read a traffic flow diagram correctly

How to identify incoming and outgoing traffic at each junction

How to write linear equations from a real-life traffic network

How traffic flow problems lead to consistent or dependent systems

This problem is important for students studying Systems of Linear Equations, Matrices, and Applications of Linear Algebra, especially for engineering mathematics and VTU exams.


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