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Student[LinearAlgebra]

 NullSpace
 compute a basis for the nullspace (kernel) of a Matrix

 Calling Sequence NullSpace(A, options)

Parameters

 A - Matrix options - (optional) parameters; for a complete list, see LinearAlgebra[NullSpace]

Description

 • The NullSpace(A) command computes a basis for the nullspace (kernel) of the linear transformation defined by Matrix A.  The result is a (possibly empty) set of Vectors.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{LinearAlgebra}}\right):$
 > $A≔⟨⟨1,2,3,4⟩|⟨5,6,7,8⟩|⟨9,10,11,12⟩|⟨13,14,15,16⟩⟩:$
 > $\mathrm{kern}≔\mathrm{NullSpace}\left(A\right)$
 ${\mathrm{kern}}{≔}\left\{\left[\begin{array}{c}{2}\\ {-3}\\ {0}\\ {1}\end{array}\right]{,}\left[\begin{array}{c}{1}\\ {-2}\\ {1}\\ {0}\end{array}\right]\right\}$ (1)
 > $\mathrm{.}\left(A,{\mathrm{kern}}_{1}\right)$
 $\left[\begin{array}{c}{0}\\ {0}\\ {0}\\ {0}\end{array}\right]$ (2)
 > $\mathrm{.}\left(A,{\mathrm{kern}}_{2}\right)$
 $\left[\begin{array}{c}{0}\\ {0}\\ {0}\\ {0}\end{array}\right]$ (3)
 > $\mathrm{NullSpace}\left(\mathrm{Id}\left(3\right)\right)$
 ${\varnothing }$ (4)