What does range(L) signify in linear algebra?

Range(L) represents the set of all possible output vectors that can be obtained by applying the linear transformation represented by the matrix L to all possible input vectors. In linear algebra, this is defined as the column space of the matrix L. The column space consists of all linear combinations of the columns of L, indicating all the vectors that can be generated by the linear transformation.

Understanding the column space is crucial because it reveals the dimensions of the output of the transformation and informs us about the rank of the matrix, which is the dimension of the column space. Thus, range(L) being equal to the column space of A correctly identifies it as the set of reachable vectors produced by the linear transformation, confirming that the correct answer is indeed the column space of A.