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Null Space Calculator

The null space calculator will quickly compute the dimension and basis of the null space of a given matrix of size up to 4x4.

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.