ULN2003 symbol is shown as if the 7 channels were inverters, but they are in fact open collector Darlington drivers.
It is a relay driver with built-in free-wheel diodes to take care of the voltage that comes from inductive loads when they turn OFF.
ULN 2003 inputs are 5V TTL level logic, and require 1mA to 1.35mA drive current from the PIC with about 2.5V threshold.
The PIC has to supply all the turn-on current, because a different supply is used to power the ULN2003 output (usually).
If you want to use ULN2003 as the driver stage for a bigger fatter final NPN transistor, you need to let the ULN2003 output drive a resistor in place of the usual relay load. When the ULN2003 is OFF, this resistor provides the base bias current to turn your NPN transistor ON. When the ULN 2003 turns ON, the base of the NPN is pulled LOW, so the matrix line is OFF.
Unless you need to drive at high frequency, I would use a power FET instead. You might even be able to not bother with the ULN2003 at all, and just switch a power FET on and OFF from the PIC output directly, or (better), use a opto-isolator driver instead.