Suppose I have a matrix $A_{3\times 3}$ then if my rank of column space is 1 then rank of null space is 2. Is there anyway I can get the basis vectors of null space from this matrix A itself?
2026-03-29 12:38:30.1774787910
Linear algebra: Null space Basis
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There is no such thing as the basis vectors of the null space, since there are infinitely many such bases. Simply solve the system$$A.\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}0\\0\\0\end{pmatrix}$$and find a basis of the space of solutions.