Sequence transformations are used for the purpose of convergence acceleration. An important algebraic property connected with a sequence transformation is its kernel, that is the set of sequences transformed into a constant sequence (usually the limit of the sequence). In this paper, we show how to construct transformations whose kernels are the sets of vector or matrix sequences of the forms x_n = x + Z_nα, x_n = x + Z_nα_n and x_n = x + Z_nα_n + Y_nβ where Z_n and Y_n are known matrices, α, α_n and β unknown vectors or matrices. Recursive algorithms for their implementation are given. Applications to the solution of systems of linear and nonlinear equations are also discussed.