Null Space and Range The null space of a linear transformation (T) is the set of vectors in the domain of T that are mapped to the zero vector (0) by T....
Null Space and Range
The null space of a linear transformation (T) is the set of vectors in the domain of T that are mapped to the zero vector (0) by T. In other words, it is the set of vectors that are left unchanged by T.
The range of a linear transformation (T) is the set of all vectors in the range of T, which is the set of all vectors that can be obtained by applying T to vectors in the domain.
The null space and range of a linear transformation are related by the following equations:
Ker(T) = {x | T(x) = 0}
Range(T) = {x | T(x) = y for some y}
where Ker(T) is the null space, Range(T) is the range, and T is the linear transformation.
The null space and range of a linear transformation are important concepts in linear algebra, as they can be used to determine the properties of a linear transformation, such as its injectivity and surjectivity