Suppose: T: R^{3}----> R^{3}is a linear transformation whose kernel has dimension 2. Describe the form of a matrix representation for T.

We did numerous examples of linear transformations from R^{3}----> R^{3}Doesn't this mean that the matrix has to be 3x3 since they all were in my class? If the kernel has dimension 2, the image has dimension 1. So isn't the only possibility of a matrix representation for T a 3x3?

Any help would be great.