Null Space Calculator
Compute the null space (kernel) of a matrix. Enter a matrix and get its null space basis vectors.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Null Space Calculator
This calculator finds the null space of a matrix by solving Ax = 0. Follow these steps:
- Set dimensions: Enter the number of Rows and Columns (1–6).
- Generate matrix: Click Generate Matrix to create input fields.
- Enter values: Fill each cell with a number (decimals allowed).
- Calculate: Click Calculate Null Space.
Result: You’ll see basis vectors for the null space. If only the zero vector exists, it’s stated. The dimension equals the number of free variables.
Tip: Use small matrices (e.g., 3×3) for clarity. All entries must be valid numbers.
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Frequently Asked Questions
The null space (or kernel) of a matrix A is the set of all vectors x such that Ax = 0. It includes the zero vector and all linear combinations of the basis vectors.
The null space is found by solving the homogeneous system Ax = 0 using Gaussian elimination to obtain the reduced row echelon form, then identifying free variables.
The dimension of the null space is the number of free variables in the system, also known as the nullity of the matrix. It relates to the rank-nullity theorem.
