# Blog

## How do you calculate the null space of a matrix? ## What is the use of matrix nullspace() in Python?

• Matrix ().nullspace () returns a list of column vectors that span the nullspace of the matrix. Returns: Returns a list of column vectors that span the nullspace of the matrix. Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.

## How do you find the nullspace of a vector?

• By definition, the nullspace of A consists of all vectors x such that A x = 0. The second row implies that x 2 = 0, and back‐substituting this into the first row implies that x 1 = 0 also. Since the only solution of A x = 0 is x = 0, the nullspace of A consists of the zero vector alone.

## What is the dimension of the null space?

• This null space is said to have dimension 3, for there are three basis vectors in this set, and is a subset of for the number of entries in each vector. Notice that the basis vectors do not have much in common with the rows of at first, but a quick check by taking the inner product of any of the rows of  