The null space of a matrix consists of all vectors mathbfx\\mathbf{x}mathbfx such that:
Amathbfx=mathbf0A\\mathbf{x} = \\mathbf{0}Amathbfx=mathbf0
Amathbfx=mathbfxA\\mathbf{x} = \\mathbf{x}Amathbfx=mathbfx
Amathbfx=lambdamathbfxA\\mathbf{x} = \\lambda\\mathbf{x}Amathbfx=lambdamathbfx
mathbfx=mathbf0\\mathbf{x} = \\mathbf{0}mathbfx=mathbf0