- Use the
**null**function to calculate orthonormal and rational**basis**vectors**for the null space**of a matrix. The**null space**of a matrix contains vectors x that satisfy Ax = 0. Create a 3-by-3 matrix of ones. This matrix is rank deficient, with two of the singular values being **Null space**of A, say N ( A) is the set of x ∈ R n such that A x = 0. It is an easy exercise to verify that it a subspace of R n. Now every vector**space**has a**basis**and the**basis**- LinearAlgebra NullSpace compute
**a basis for the nullspace**(kernel) of a Matrix Calling Sequence Parameters Description Examples Calling Sequence NullSpace( A , options ) Parameters A - Matrix options - (optional); constructor options for the result object... - THE
**NULL SPACE**OFA. The**null space**of Ais a subspace of Rn. We will denote this subspace by N(A). Here is the deﬁnition: N(A) = {X :AX= 0 m} THEOREM. If Ais an m×nmatrix, then N(A) is a subspace of Rn. Proof. First of all, notice that if X is in N(A), then AX = 0 m. Since Ais m× nand AX is m×1, it follows that X must be n×1. That is, X is ... - Example:
**A basis for the null space**of a 2 by 3 matrix A is given by 1 1 2 Give the rank of A. Example: The RREF of the matrix A is 11 0 00 1 000 Give the rank of A, the nullity of A, and**a basis for the null space**of A.