Practice Redundancy in Math

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

Quick Recap

An equation in a system that is a linear combination of the others and therefore adds no new constraints or information.

If equation 2 is just equation 1 doubled, it's redundant — the same constraint stated twice.

easy

In \begin{cases} x + y = 3 \\ 2x + 2y = 6 \end{cases}, is the second equation redundant?

medium

In \begin{cases} x + y = 2 \\ 2x - y = 1 \\ 3x = 3 \end{cases}, is equation 3 redundant?

easy

Is y = 2x + 1 redundant in \begin{cases} y = 2x + 1 \\ y = -x + 4 \end{cases}?

medium

If a 3 \times 3 system has rank 2, how many redundant equations are there?