Final answer:
The columns of an invertible 3x3 matrix span R³ because they represent linear combinations of the basis vectors.
Step-by-step explanation:
An invertible 3x3 matrix is a matrix that has an inverse, which means it can be multiplied by another matrix to give the identity matrix. In the context of linear algebra, the columns of a matrix represent the linear combinations of the basis vectors. Since an invertible matrix has a set of linearly independent columns, these columns span the entire vector space R³. This means that any vector in R³ can be expressed as a linear combination of the columns of the invertible matrix.