How does the Null Space Calculator work?

Solve Ax = 0 using row reduction (RREF) Then: Free variables correspond to null space dimensions Then: Rank-nullity theorem: rank + nullity = n (columns) Then: Null space is always a subspace containing the zero vector.

Can you give an example of how to use the Null Space Calculator?

Example: Input [[1,2,3],[4,5,6]] × x = 0 gives a result of Null space has dimension 1; one free variable.

Is the Null Space Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Null Space Calculator?

Our Null Space Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Null Space Calculator

Matrix (one row per line)

The null space (kernel) of a matrix A is the set of all vectors x such that Ax = 0. The nullity is the dimension of the null space. Understanding null space is essential in solving linear systems and linear algebra.

Symbol	Name	Unit	Description
A	matrix	—	—
x	vector in null space	—	—
Null(A)	null space (kernel) of A	—	—

Matrix	Rank	Nullity	Free variables
3×3 full rank	3	0	0
3×3 rank 2	2	1	1
2×4 rank 2	2	2	2
Identity n×n	n	0	0

References

›Null space — Khan Academy

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Null Space Calculator

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