Null Space Calculator (2×2)
The Null Space Calculator finds the nullity and a basis for the null space (kernel) of a 2×2 matrix. Enter the four matrix entries.
Formula
Null space = all v with A·v = 0; nullity = 2 − rank
- If the determinant is non-zero, the only solution is the zero vector.
- For a rank-1 matrix, the null space is a single line through the origin.
[[1,2],[2,4]]
Inputs
- a₁₁: 1
- a₁₂: 2
- a₂₁: 2
- a₂₂: 4
det 0, rank 1 → null space is span{(−2, 1)}, nullity 1.
Frequently asked questions
What is the null space?
The set of all vectors the matrix maps to zero. Its dimension is the nullity.