The Safety Board's full report on this investigation is provided as Aviation Accident Report number AAR-87/07. To obtain a copy of this report, or to view the executive summary online, please see the Web site at http://www.ntsb.gov/publictn/publictn.htm AT APRX 1140 PDT, A PIPER PA-28, N4891F, DEPARTED TORRANCE, CA ON A VFR FLT TO BIG BEAR, CA. AFTER TAKEOFF, THE PLT TURNED EASTBOUND TWD THE PARADISE VORTAC WITH HIS X-PONDER SQUAWKING 1200. AT THAT TIME, AEROMEXICO FLT 498 (DC-8, MEX REGISTRY XA-JED) WAS ON ARRIIVAL, RCVG NORTHBOUND VECTORS FM LAX APCH CTL (AR-1 CTLR) FOR AN ILS APCH TO THE LAX INTL ARPT. AT 1151:04, THE CTLR ASKED FLT 498 TO RDC SPD TO 190 KTS & DSCND FM 7000' TO 6000'. DRG THIS TIME, THE CTLR WAS CTLG OTR TRAFFIC & PROVIDING RADAR ADVISORIES, BUT DIDN'T SEE A DISPLAY FOR N4891F ON HIS SCOPE. AT 1152:09, N4891F & FLT 498 CONVERGED & COLLIDED AT APRX 6560', THEN FELL TO THE GND. AN INV REVEALED N4891F HAD INADVERTENTLY ENTERED THE LAX TERMINAL CONTROL AREA (TCA) & WASN'T IN RADIO CONTACT WITH ATC. LAX TRACON WASN'T EQUIPPED WITH AN AUTO CONFLICT ALERT SYS & THE ANALOG BEACON RESPONSE FM N4891F'S X-PONDER WASN'T DISPLAYED DUE TO EQUIP CONFIGURATION. N4891F'S PSN WAS DISPLAYED BY AN ALPHANUMERIC TRIANGLE, BUT THE PRIMARY TARGET WASN'T DISPLAYED DUE TO AN ATMOSPHERIC INVERSION.