Þ™ "“"Nè™ " ™YOU SHOULD HAVE A GOOD WORKING KNOWLEDGE OF LOWER ORDER"™L™ " DETERMINANTS AND THEIR EQUATION FORMS BEFORE USING THIS PROGRAM. "¥°™ ""… " HIT TO CONTINUE, TO QUIT "; I$x‹ I$ ² "N" § ™ "“Ÿ": €%ª™ "“",Üþ%S@ *******************************z¤ ** SOLVE A SYSTEM OF FOUR **¡ ** EQUATIONS BY DETERMINANTS **Èl *******************************ÒЙ "›"ü4ˆ E$ ² " A1X + B1Y + C1Z + D1T = E1 "&˜ˆ F$ ² " A2X + B2Y + C2Z + D2T = E2 "Püˆ G$ ² " A3X + B3Y + C3Z + D3T = E3 "z` ˆ H$ ² " A4X + B4Y + C4Z + D4T = E4 "½Ä ™ " SOLVE A SYSTEM OF FOUR LINEAR EQUATIONS BY DETERMINANTS "è( ™ " THE EQUATIONS ARE IN THE FORM : "Œ ™ " "; E$@ð ™ " "; F$lT ™ " "; G$˜¸ ™ " "; H$¢ ™ ""·€ ™ "WHERE: "Áä ™ "›"ÛH ™ " IN EQUATION ONE " ¬ ™ " A1 IS THE COEFFICIENT OF X "E ™ " B1 IS THE COEFFICIENT OF Y "z t™ " C1 IS THE COEFFICIENT OF Z "¯ Ø™ " D1 IS THE COEFFICIENT OF T "á <™ " AND E1 IS THE CONSTANT. "ü  ™ " IN EQUATION TWO "1!™ " A2 IS THE COEFFICIENT OF X "f!h™ " B2 IS THE COEFFICIENT OF Y "›!Ì™ " C2 IS THE COEFFICIENT OF Z "Ð!0™ " D2 IS THE COEFFICIENT OF T ""”™ " AND E2 IS THE CONSTANT. " "ø™ "‘™"h"\… " HIT TO CONTINUE, TO QUIT "; J$ƒ"À‹ J$ ² "N" § ™ "“Ÿ": €"$™ "›"°"ˆ™ "“"é"ì™ " "; E$"#P™ " "; F$[#´™ " "; G$”#™ " "; H$ž#|™ ""º#à™ " IN EQUATION THREE "ñ#D™ " A3 IS THE COEFFICIENT OF X "($¨™ " B3 IS THE COEFFICIENT OF Y "_$ ™ " C3 IS THE COEFFICIENT OF Z "–$p™ " D3 IS THE COEFFICIENT OF T "Ê$Ô™ " AND E3 IS THE CONSTANT. "à$8™ "AND:› "û$œ™ " IN EQUATION FOUR2%™ " A4 IS THE COEFFICIENT OF X "i%d™ " B4 IS THE COEFFICIENT OF Y " %È™ " C4 IS THE COEFFICIENT OF Z "×%,™ " D4 IS THE COEFFICIENT OF T " &™ " AND E4 IS THE CONSTANT. "&ô™ "™"q&X… " HIT TO CONTINUE, TO QUIT "; K$Œ&¼‹ K$ ² "N" § ™ "“Ÿ": €¿& ™ " “ FOR EXAMPLE:›"ù&„™ " ‘"; E$2'è™ " "; F$k'L™ " "; G$¤'°™ " "; H$ª'âì'™ " šX + 2Y + Z + 6T = 5›(EQUATION ONE) ".(x™ " –2X + 3Y + 8Z + 2T = 1›(EQUATION TWO) "r(Ü™ " žX - 5Y + 3Z + 4T = -6›(EQUATION THREE) "µ(@™ " 4X - Y + 5Z - 2T = 0›(EQUATION FOUR) ")¤™ " A1 IS š1›, B1 IS š2›, C1 IS š1›, D1 IS š6›, AND E1 IS š5›. "T) ™ "A2 IS –2›, B2 IS –3›, C2 IS –8›, D2 IS –2›, AND E2 IS –1›. "¥)l ™ "A3 IS ž1›, B3 IS ž-5›, C3 IS ž3›, D3 IS ž4›, AND E3 IS ž-6›. "ö)Ð ™ "A4 IS 4›, B4 IS -1›, C4 IS 5›, D4 IS -2›, AND E4 IS 0›. "*4!™ "™"\*˜!… " HIT TO CONTINUE, TO QUIT "; L$w*ü!‹ L$ ² "N" § ™ "“Ÿ": €š*`"™ "“"¤*Ä"™ "›"ø*(#™ " THE PROGRAM WILL PRINT ANSWERS IN BOTH FRACTIONAL AND DECIMAL "A+Œ#™ "FORM TO SATISFY YOUR PARTICULAR REQUIREMENT. "`+ð#™ " ENTER COEFFICIENTS "—+T$™ " š(EQUATION ONE)› "¡+¸$™ "‘"»+%… " A1 = "; A1Õ+€%… " B1 = "; B1ï+ä%… " C1 = "; C1 ,H&… " D1 = "; D1#,¬&… " E1 = "; E1a,'™ " –(EQUATION TWO)› ": ™ "‘"{,t'… " A2 = "; A2•,Ø'… " B2 = "; B2¯,<(… " C2 = "; C2É, (… " D2 = "; D2ã,)… " E2 = "; E2"-h)™ " ž(EQUATION THREE)›": ™ "‘"<-Ì)… " A3 = "; A3V-0*… " B3 = "; B3p-”*… " C3 = "; C3Š-ø*… " D3 = "; D3¤-\+… " E3 = "; E3â-À+™ " (EQUATION FOUR)›": ™ "‘"ü-$,… " A4 = "; A4.ˆ,… " B4 = "; B40.ì,… " C4 = "; C4J.P-… " D4 = "; D4d.´-… " E4 = "; E4o..™ "™‘"Å.|.… " TYPE IF CORRECT, IF NOT "; M$ä.à.‹ M$ ² "N" § 8800: Õ 12100ê.D/_/¨/ˆ A ² A1 ¬ ((B2 ¬ C3 ¬ D4) ª (C2 ¬ D3 ¬ B4) ª (D2 ¬ B3 ¬ C4) « (B4 ¬ C3 ¬ D2) « (C4 ¬ D3 ¬ B2) « (D4 ¬ B3 ¬ C2))e/ 0Û/p0ˆ B ² «A2 ¬ ((B1 ¬ C3 ¬ D4) ª (C1 ¬ D3 ¬ B4) ª (D1 ¬ B3 ¬ C4) « (B4 ¬ C3 ¬ D1) « (C4 ¬ D3 ¬ B1) « (D4 ¬ B3 ¬ C1))á/Ô0V081ˆ C ² A3 ¬ ((B1 ¬ C2 ¬ D4) ª (C1 ¬ D2 ¬ B4) ª (D1 ¬ B2 ¬ C4) « (B4 ¬ C2 ¬ D1) « (C4 ¬ D2 ¬ B1) « (D4 ¬ B2 ¬ C1))\0œ1Ò02ˆ E ² «A4 ¬ ((B1 ¬ C2 ¬ D3) ª (C1 ¬ D2 ¬ B3) ª (D1 ¬ B2 ¬ C3) « (B3 ¬ C2 ¬ D1) « (C3 ¬ D2 ¬ B1) « (D3 ¬ B2 ¬ C1))ê0d2ˆ D ² A ª B ª C ª Eð0È2e1,3ˆ F ² E1 ¬ ((B2 ¬ C3 ¬ D4) ª (C2 ¬ D3 ¬ B4) ª (D2 ¬ B3 ¬ C4) « (B4 ¬ C3 ¬ D2) « (C4 ¬ D3 ¬ B2) « (D4 ¬ B3 ¬ C2))k13á1ô3ˆ G ² «E2 ¬ ((B1 ¬ C3 ¬ D4) ª (C1 ¬ D3 ¬ B4) ª (D1 ¬ B3 ¬ C4) « (B4 ¬ C3 ¬ D1) « (C4 ¬ D3 ¬ B1) « (D4 ¬ B3 ¬ C1))ç1X4\2¼4ˆ H ² E3 ¬ ((B1 ¬ C2 ¬ D4) ª (C1 ¬ D2 ¬ B4) ª (D1 ¬ B2 ¬ C4) « (B4 ¬ C2 ¬ D1) « (C4 ¬ D2 ¬ B1) « (D4 ¬ B2 ¬ C1))b2 5Ø2„5ˆ I ² «E4 ¬ ((B1 ¬ C2 ¬ D3) ª (C1 ¬ D2 ¬ B3) ª (D1 ¬ B2 ¬ C3) « (B3 ¬ C2 ¬ D1) « (C3 ¬ D2 ¬ B1) « (D3 ¬ B2 ¬ C1))ñ2è5ˆ X1 ² F ª G ª H ª I÷2L6l3°6ˆ J ² A1 ¬ ((E2 ¬ C3 ¬ D4) ª (C2 ¬ D3 ¬ E4) ª (D2 ¬ E3 ¬ C4) « (E4 ¬ C3 ¬ D2) « (C4 ¬ D3 ¬ E2) « (D4 ¬ E3 ¬ C2))r37è3x7ˆ K ² «A2 ¬ ((E1 ¬ C3 ¬ D4) ª (C1 ¬ D3 ¬ E4) ª (D1 ¬ E3 ¬ C4) « (E4 ¬ C3 ¬ D1) « (C4 ¬ D3 ¬ E1) « (D4 ¬ E3 ¬ C1))î3Ü7c4@8ˆ L ² A3 ¬ ((E1 ¬ C2 ¬ D4) ª (C1 ¬ D2 ¬ E4) ª (D1 ¬ E2 ¬ C4) « (E4 ¬ C2 ¬ D1) « (C4 ¬ D2 ¬ E1) « (D4 ¬ E2 ¬ C1))i4¤8ß49ˆ M ² «A4 ¬ ((E1 ¬ C2 ¬ D3) ª (C1 ¬ D2 ¬ E3) ª (D1 ¬ E2 ¬ C3) « (E3 ¬ C2 ¬ D1) « (C3 ¬ D2 ¬ E1) « (D3 ¬ E2 ¬ C1))ø4l9ˆ Y1 ² J ª K ª L ª Mþ4Ð9s54:ˆ N ² A1 ¬ ((B2 ¬ E3 ¬ D4) ª (E2 ¬ D3 ¬ B4) ª (D2 ¬ B3 ¬ E4) « (B4 ¬ E3 ¬ D2) « (E4 ¬ D3 ¬ B2) « (D4 ¬ B3 ¬ E2))y5˜:ï5ü:ˆ O ² «A2 ¬ ((B1 ¬ E3 ¬ D4) ª (E1 ¬ D3 ¬ B4) ª (D1 ¬ B3 ¬ E4) « (B4 ¬ E3 ¬ D1) « (E4 ¬ D3 ¬ B1) « (D4 ¬ B3 ¬ E1))õ5`;j6Ä;ˆ P ² A3 ¬ ((B1 ¬ E2 ¬ D4) ª (E1 ¬ D2 ¬ B4) ª (D1 ¬ B2 ¬ E4) « (B4 ¬ E2 ¬ D1) « (E4 ¬ D2 ¬ B1) « (D4 ¬ B2 ¬ E1))p6(<æ6Œ<ˆ Q ² «A4 ¬ ((B1 ¬ E2 ¬ D3) ª (E1 ¬ D2 ¬ B3) ª (D1 ¬ B2 ¬ E3) « (B3 ¬ E2 ¬ D1) « (E3 ¬ D2 ¬ B1) « (D3 ¬ B2 ¬ E1))ÿ6ð<ˆ Z1 ² N ª O ª P ª Q7T=z7¸=ˆ R ² A1 ¬ ((B2 ¬ C3 ¬ E4) ª (C2 ¬ E3 ¬ B4) ª (E2 ¬ B3 ¬ C4) « (B4 ¬ C3 ¬ E2) « (C4 ¬ E3 ¬ B2) « (E4 ¬ B3 ¬ C2))€7>ö7€>ˆ S ² «A2 ¬ ((B1 ¬ C3 ¬ E4) ª (C1 ¬ E3 ¬ B4) ª (E1 ¬ B3 ¬ C4) « (B4 ¬ C3 ¬ E1) « (C4 ¬ E3 ¬ B1) « (E4 ¬ B3 ¬ C1))ü7ä>q8H?ˆ U ² A3 ¬ ((B1 ¬ C2 ¬ E4) ª (C1 ¬ E2 ¬ B4) ª (E1 ¬ B2 ¬ C4) « (B4 ¬ C2 ¬ E1) « (C4 ¬ E2 ¬ B1) « (E4 ¬ B2 ¬ C1))w8¬?í8@ˆ V ² «A4 ¬ ((B1 ¬ C2 ¬ E3) ª (C1 ¬ E2 ¬ B3) ª (E1 ¬ B2 ¬ C3) « (B3 ¬ C2 ¬ E1) « (C3 ¬ E2 ¬ B1) « (E3 ¬ B2 ¬ C1))9t@ˆ T1 ² R ª S ª U ª V 9Ø@/9¤Q ** PROGRAM YOU WILL HAVE TO WATCH THE LIMITS FOR **{>R ** CHARACTERS PER LINE. I USED THE 128 AND HAD TO **¼>lR ** DIVIDE EACH FORMULA INTO FOUR PARTS! THEN I WAS **ý>ÐR ** ABLE TO ADD EACH OF THE FOUR PARTS TO GET THE **>?4S ** ANSWER FOR EACH OF THE FOUR UNKNOWNS. TRY NOT TO **?˜S ** GET ALL THE RESULTING VARIABLES CONFUSED! AND, **À?üS ** AGAIN, THE DISPLAY MUST BE MODIFIED TO SUPPORT THE **@`T ** C-64'S 40 COLUMNS. **B@ÄT *********************************************************H@(U‰@ŒU *********************************************************Ê@ðU ** THIS PROGRAM WAS WRITTEN BY STEPHAN (STEVE) BURDIN ** ATV ** AND IS WHOLLY INTENDED FOR USE IN THE PUBLIC DOMAIN.**LA¸V ** NOTE: I HOPE YOU FIND THIS PROGRAM USEFUL AND **AW ** PLEASANT TO USE. IT IS THE THIRD ONE IN A SERIES. **ÎA€W ** ABOUT THAT FOURTH VARIABLE: T, I DIDN'T REALLY WANT **BäW ** TO USE THAT LETTER BECAUSE IT'S DIFFICULT TO **PBHX ** DISTINGUISH, ESPECIALLY NEXT TO THE NUMBER 1. ANY- **‘B¬X ** WAY, I USED IT BECAUSE IT SEEMS TO BE THE VARIABLE **ÒBY ** YOU WILL SEE USED IF YOU LOOK IN MATHEMATICS TEXTS. **CtY ** WHAT TO LOOK FOR NEXT? I'M NOT SURE. MAYBE I'LL **TCØY ** DO A SIMPLER ONE NEXT. SOMETHING LIKE QUADRATICS **•C