Two-vector linear independence calculator

Reviewed by the CalculatorHub team, edited by James Graham. Method from NIST DLMF. Last verified 2026-06-23.

The Two-vector linear independence calculator computes two-vector linear independence from the relation independent iff a d - b c != 0. It takes 4 inputs (v1 x, v1 y, v2 x, v2 y) and returns the independent?. Because this is a pure mathematical or physical formula rather than a jurisdiction-specific rule, the result never changes over time: the same inputs always produce the same answer, so you can rely on it whether you are checking homework, sizing a design, or sanity-checking another tool. Enter your values in the fields below and the result updates instantly; you can also share a permalink that pre-fills the exact calculation, which is useful for teaching, reports, or collaboration. For example, with v1 x = 1, v1 y = 2, v2 x = 2, v2 y = 4, the independent? works out to dependent, and the worked example further down the page shows every step so you can follow the arithmetic and reproduce it by hand. The method is the standard form documented by NIST DLMF, and the figure above each result carries the date it was last verified. This tool is general information and is not a substitute for professional engineering, medical, financial, or scientific advice; always check critical results against the primary source and your own judgement.