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Linear Independence Calculator

The linear independence calculator is here to check whether your vectors are linearly independent and tell you the dimension of the space they span.

One row per line, values separated by commas or spaces.
Clear
Rank2the number of pivots
Size3×3
Pivot columns1, 2
Free columns1
Nullity1dimension of the null space
Full rank?No

Reduced row echelon form

10-1
012
000

The method

Gauss–Jordan elimination to reduced row echelon form

Rank answers most questions

The number of pivots after reduction is the rank — the dimension of the space the matrix actually reaches. Full rank means the columns are linearly independent and, for a square matrix, that an inverse exists. The nullity (columns minus rank) counts the independent directions the matrix crushes to zero.