Degrees of Freedom Math Example 1

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

Example 1

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

Solution

  1. 1
    Step 1: Apply DOF=n−r\text{DOF} = n - r where n=3n = 3 variables, r=2r = 2 equations.
  2. 2
    Step 2: DOF=3−2=1\text{DOF} = 3 - 2 = 1.
  3. 3
    This means the solution is a line (one free parameter).

Answer

11 degree of freedom
Degrees of freedom tells you the dimension of the solution space. With 1 DOF, you can freely choose one variable and the others are determined — the solutions form a line in 3D space.

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 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?

Example 4 medium

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

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