The Argentine ship blew up after seven hits ignited her cargo of jet fuel and ammunition.
The Taiwanese vessel refused to respond to warnings from the patrol ship and then abruptly turned toward the Argentine ship, said military officials.
They were later rescued by an Argentine ship.
She ordered the sinking of an Argentine ship, the Belgrano, that was sailing away from the exclusion zone.
Two Argentine ships, a tug with rescue equipment and an icebreaker, are steaming to the scene and are expected to arrive today.
These dispatches urged that certain Argentine ships should be "spurlos versenkt" - destroyed without a trace.
All hands were rescued by an Argentine ship.
The Quidora torpedo Boat approached and ordered the Argentine ship to leave the area.
The Argentine ship made its way to freedom on its own.
British air and naval vessels have been patrolling the zone since then, barring entry to Argentine ships and aircraft.