Linear Independence Calculator

Your details

How many vectors are in your set.
The number of components in each vector (the dimension of the ambient space).
ResultIndependent
Linearly Independent

Whether the set of vectors is linearly independent or dependent.

Rank of the matrix3
Dimension of the span3
Pivot count3
Determinant (square case)1
Rank (pivots)3
Span dimension3

Linearly Independent: the vectors form a basis-ready set.

  • All 3 vectors are linearly independent: none of them can be written as a linear combination of the others.
  • They span a 3-dimensional subspace of 3-dimensional space.
  • Because you have 3 independent vectors in 3-dimensional space, they form a basis for that entire space.

Next stepTo extend to a full basis for a larger space, add more vectors and re-run the check.

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