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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

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{LinearAlgebra}]\right):$
 > $A≔⟨⟨1,2,3,4⟩|⟨5,6,7,8⟩|⟨9,10,11,12⟩|⟨13,14,15,16⟩⟩:$
 > $\mathrm{kern}≔\mathrm{NullSpace}\left(A\right)$
 ${\mathrm{kern}}{≔}\left\{\left[\begin{array}{r}{2}\\ {-}{3}\\ {0}\\ {1}\end{array}\right]{,}\left[\begin{array}{r}{1}\\ {-}{2}\\ {1}\\ {0}\end{array}\right]\right\}$ (1)
 > $A\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{kern}}_{1}$
 $\left[\begin{array}{r}{0}\\ {0}\\ {0}\\ {0}\end{array}\right]$ (2)
 > $A\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{kern}}_{2}$
 $\left[\begin{array}{r}{0}\\ {0}\\ {0}\\ {0}\end{array}\right]$ (3)
 > $\mathrm{NullSpace}\left(\mathrm{Id}\left(3\right)\right)$
 $\left\{{}\right\}$ (4)