Variational and bivariational functionals are used to derive bounds on the entries of the inverse of a real non-singular matrix. Bounds are given for both the symmetric and non-symmetric case. In the symmetric and positive definite case, the Kantorovich inequality and Weilandt inequality are available for providing such bounds. The bounds we derive can not be obtained using these established inequalities and in a number of examples our bounds are found to be tighter when simple trial vectors are used. For the non-symmetric case, the bounds we derive are of uncertain value as there is little with which to compare them.