Practice Degrees of Freedom in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

If x + y = 10, you can choose x freely, but then y is fixed. One degree of freedom.

easy

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

medium

The system \begin{cases} x + y + z = 6 \\ x + y + z = 6 \\ 2x - y = 1 \end{cases} has 3 equations and 3 variables. Does it have 0 degrees of freedom?

easy

How many DOF does a single equation x + y = 5 have?

medium

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