The null space of a matrix is the set of all vectors that, when multiplied by the matrix, result in the zero vector. This means that these vectors do not contribute any information to the transformation represented by the matrix. The null space is important in linear algebra because it helps identify solutions to homogeneous equations, where the output is zero. In practical terms, the null space can reveal dependencies among the columns of a matrix. If the null space contains only the zero vector, the matrix is said to have full rank, indicating that its columns are linearly independent. Understanding the null space is crucial for solving systems of equations and analyzing linear transformations.