Null Space Calculator
Calculate the null space (kernel) of a matrix, find basis vectors, rank, and nullity.
Matrix Input
Matrix A
Rank
2
Nullity
1
Null Space Basis
v1 = (1.0000, -2.0000, 1.0000)
Dimension Theorem
rank(A) + nullity(A) = 2 + 1 = 3 = 3 (number of columns)
Pivot Columns: 1, 2
Free Variables: columns 3
RREF of A
1.000.00-1.00
0.001.002.00
Verification (A × v = 0)
A × v1 = (0.0000, 0.0000)
About Null Space
Definition
The null space (kernel) of A is the set of all vectors x such that Ax = 0.
Rank-Nullity Theorem
rank(A) + nullity(A) = number of columns of A
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
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Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun
🔄Last reviewed: May 2026
✓Formula checks are based on standard references and internal QA review.