Degrees of Freedom Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
A system of 4 equations in 4 unknowns has rank 3. How many DOF?

Solution

  1. 1
    DOF =n−r=4−3=1= n - r = 4 - 3 = 1.
  2. 2
    One of the 4 equations is a linear combination of the others.

Answer

11 degree of freedom
The rank of a system is the number of independent equations. Even with 4 equations, if one is redundant (rank 3), there's still a free variable giving infinitely many solutions.

About Degrees of Freedom

The number of independent values that remain free to be chosen after all constraints in a system have been satisfied.

Learn more about Degrees of Freedom →

More Degrees of Freedom Examples

Example 1 easy

A system has 3 variables and 2 independent equations. How many degrees of freedom?

Example 2 medium

The system [formula] has 3 equations and 3 variables. Does it have 0 degrees of freedom?

Example 3 easy

How many DOF does a single equation [formula] have?

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