Null Space Calculator
Find the basis for the null space (kernel) of a matrix.
The null space (or kernel) of a matrix A is the set of all vectors x such that Ax = 0. This calculator finds a basis for that space.
Calculator Inputs
Enter rows separated by semicolons (;), values by commas (,)
Results
Enter values above to see your results
How It Works
We perform Gaussian elimination to bring the matrix to Reduced Row Echelon Form (RREF), identify free variables, and construct the basis vectors.
Worked Examples
Matrix A = [[1, 2], [2, 4]]
[[1, 2], [0, 0]]= Row Reducex₁ + 2x₂ = 0= x₁ = -2x₂[-2, 1]= Free var x₂Tips & Best Practices
- •Enter matrix row by row: "1,2; 3,4" for a 2x2.
- •If the null space contains only the zero vector, the nullity is 0.
Frequently Asked Questions
What is Nullity?
Nullity is the dimension of the null space, which equals the number of free variables (Total Columns - Rank).
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