1. The problem statement, all variables and given/known data Let T be a Linear Transformation defined on R4 ---> R4 Is that true that the following is always true ? KerT + ImT = R4 2. Relevant equations 3. The attempt at a solution Since every vector in R4 must be either in KerT or the ImT, so the addition of those subspace contains R. and ofc every vector in ImT or KerT is in R4.