Due to the significant role played by singular systems in the form E ¿ x ( t ) = Ax ( t ) , on mathematical modeling of science and engineering problems; in the last years recent years its interest in the descriptive analysis of its structural and dynamic properties. However, much less effort has been devoted to studying the exact con- trollability by measuring the minimum set of controls needed to direct the entire system E ¿ x ( t ) = Ax ( t ) to any desired state. In this work, we focus the study on obtaining the set of all matrices B with a minimal number of columns, by making the singular system E ¿ x ( t ) = Ax ( t ) + Bu ( t ) controllable.