5.2: Kernel and Image of a Linear Transformation. 1. Linear transformation.ppt 1. Suppose the following chain of matrices is given. Kernel, Rank, Range We now study linear transformations in more detail. Now we can prove that every linear transformation is a matrix transformation, and we will show how to compute the matrix. Find the kernel of the linear transformation L: V → W. SPECIFY THE VECTOR SPACES. FINDING A BASIS FOR THE KERNEL OR IMAGE. The range of a linear transformation f : V !W is the set of vectors the linear transformation maps to. ex. Furthermore, the kernel of T is the null space of A and the range of T is the column space of A. Composition of a Linear Transformations. Furthermore, [T A] = [T A] E m E n = A, since the representation of vectors as n-tuples of elements in k is the same as expressing each vector under the standard basis (ordered) in the vector space k n. Below we list some of the basic properties: say a linear transformation T: