Test whether a set of vectors is linearly independent by reducing the vector matrix to rank.
Last updated: June 2026 | By Patchworkr Team
A set of vectors is linearly independent when no vector in the set can be written as a linear combination of the others. If one vector can be built from the rest, the set is dependent.
The vectors [1, 0] and [0, 1] form the identity matrix, so their rank is 2 and the set is independent.
What happens if there are more vectors than dimensions?
The set must be dependent because the rank can never exceed the dimension of the space.
Does the calculator accept decimals?
Yes. Any finite real coordinate is accepted, including decimal and scientific notation values.
Why use rank instead of only determinants?
Rank works for any matrix shape, not just square matrices, so it gives a more complete test.
What if the vectors are all zeros?
A zero vector makes the set dependent because it can be written as a trivial combination of the others.
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