  A badly approximable system of affine forms is determined by a matrix and a
vector. We show Kleinbock's conjecture for badly approximable systems of affine
forms: for any fixed vector, the set of badly approximable systems of affine
forms is winning (in the sense of Schmidt games) even when restricted to a
fractal (from a certain large class of fractals). In addition, we consider
fixing the matrix instead of the vector where an analog statement holds.
