Linear Independence Calculator
Check if a set of vectors is linearly independent, find rank, and determine if they form a basis.
Input Vectors
v1
v2
v3
Linear Independence
Linearly Independent
Rank = 3
Spans R3?
Yes
Forms Basis?
Yes
RREF of Vector Matrix
1.000.000.00
0.001.000.00
0.000.001.00
Summary
- Number of vectors: 3
- Vector dimension: 3
- Rank: 3
- Pivot columns: 1, 2, 3
Linear Independence
Definition
Vectors are linearly independent if no vector can be written as a linear combination of the others.
Key Facts
- n vectors in Rⁿ are independent iff rank = n
- More than n vectors in Rⁿ are always dependent
- Independent + spanning = basis