Enter the total number of columns and the rank into the calculator to determine the nullity of a matrix. This calculator can also evaluate any of the variables given the others are known.

## Matrix Nullity Formula

The following formula is used to calculate the nullity of a matrix.

Nullity(M) = n - Rank(M)

Variables:

• Nullity(M) is the nullity of the matrix M n is the total number of columns in the matrix M Rank(M) is the rank of the matrix M

To calculate the nullity of a matrix, subtract the rank of the matrix from the total number of columns in the matrix. The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. The nullity of a matrix is the dimension of the null space of the matrix, which is the set of all vectors that when multiplied by the matrix, result in the zero vector.

## What is a Matrix Nullity?

Matrix nullity refers to the dimension of the null space of a matrix, which is the set of all vectors that, when multiplied by the matrix, result in a zero vector. In other words, it is the number of linearly independent solutions to the homogeneous equation Ax = 0. The nullity of a matrix can provide important information about the matrix’s properties and its rank.