This paper investgates th“bottleneck”problems about linear feed forward network classifiers （LFNC） for supervised learning. It is proved that some hidden layer in the LFNC with hidden node number less than the rank of the within dispersion matrix can do the Fisher linear transformation of the pattern samples from the previous layer

and the mechanism of producing bottleneck in the linear classifiers is disclosed and the method to solve it is presented. Finally

as an approach to capabilities of suth classifiers

it is propose applying the linear supervised classifiers to solving the inversion of nonsingular matrix. The computation results of two given examples show that the method to apply the linear supervised network to the inversion of nonsingular matrix is very effective.