Rank of the Linear Transformation T
Rank of a linear transformation is defined as the dimension of the image (or range) of the transformation. In other words, it is the dimension of the subspace spanned by the columns of the matrix representing the transformation.

Transformation T
The linear transformation T(x, y, z) = (x/2, y/2, z/2) can be represented by the matrix [1/2 0 0; 0 1/2 0; 0 0 1/2] where each column corresponds to the output of the transformation on the standard basis vectors of R³.

Rank of T
Since the matrix representing the transformation T has all non-zero rows, the rank of T is equal to the number of non-zero rows in the matrix. In this case, all rows are non-zero, so the rank of T is 3.

Explanation
The rank of T being 3 implies that the transformation T is onto, meaning that the image of T spans all of R³. This makes sense intuitively since T scales each component of the input vector by 1/2, so any vector in R³ can be obtained as an output of T.
In conclusion, the rank of the linear transformation T(x, y, z) = (x/2, y/2, z/2) is 3, indicating that the transformation spans all of R³.