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5000*a + 2000*b + 2000*c + 1000*d + 0*E + 900*f + 3000*g + 1000*h + 3000*y + 2500*x + 450*k + 2800*l + 1000*m + 2000*n + 2000*o + 1000*p + 500*q + 1500*r + 0*s + 0*t + 0*u + 0*v = 582925
6000*a + 2000*b + 2000*c + 1300*d + 0*E + 500*f + 2000*g + 600*h + 2000*y + 1500*x + 1000*k + 3000*l + 2000*m + 2500*n + 2000*o + 1000*p + 1000*q + 1000*r + 0*s + 0*t + 0*u + 0*v = 594400
6500*a + 3000*b + 3000*c + 2000*d + 0*E + 1500*f + 4500*g + 1500*h + 2500*y + 3500*x + 2000*k + 4000*l + 1500*m + 4000*n + 1500*o + 1000*p + 1000*q + 1500*r + 0*s + 0*t + 0*u + 0*v = 809200
=
$$- frac{31 f}{160} – frac{19 g}{4} – frac{7 h}{4} + frac{69 k}{320} + frac{l}{20} – 2 m + frac{21 n}{16} – frac{29 o}{16} – frac{7 p}{16} – frac{47 q}{32} – frac{7 r}{32} – frac{63 x}{32} – frac{7 y}{4} + frac{196439}{640}$$
=
306.9359375 + 1.3125*n + 0.05*l + 0.215625*k – 2*m – 0.21875*r – 0.4375*p – 1.75*h – 1.75*y – 4.75*g – 1.8125*o – 1.46875*q – 1.96875*x – 0.19375*f
$$b_{1} = – frac{377 f}{320} + frac{17 g}{16} + frac{3 h}{8} + frac{223 k}{640} – frac{19 l}{20} + frac{59 m}{16} – frac{49 n}{32} + frac{41 o}{32} + frac{3 p}{32} + frac{143 q}{64} – frac{89 r}{64} – frac{89 x}{64} – frac{21 y}{16} – frac{78011}{1280}$$
=
$$- frac{377 f}{320} + frac{17 g}{16} + frac{3 h}{8} + frac{223 k}{640} – frac{19 l}{20} + frac{59 m}{16} – frac{49 n}{32} + frac{41 o}{32} + frac{3 p}{32} + frac{143 q}{64} – frac{89 r}{64} – frac{89 x}{64} – frac{21 y}{16} – frac{78011}{1280}$$
=
-60.94609375 + 0.09375*p + 0.375*h + 1.0625*g + 1.28125*o + 3.6875*m + 2.234375*q + 0.3484375*k – 1.3125*y – 1.53125*n – 1.390625*r – 1.390625*x – 1.178125*f – 0.95*l
$$a_{1} = frac{49 f}{160} + frac{5 g}{8} + frac{h}{4} + frac{49 k}{320} – frac{l}{5} – frac{5 m}{8} + frac{n}{16} – frac{9 o}{16} – frac{3 p}{16} – frac{7 q}{32} + frac{r}{32} + frac{17 x}{32} – frac{y}{8} + frac{4047}{128}$$
=
$$frac{49 f}{160} + frac{5 g}{8} + frac{h}{4} + frac{49 k}{320} – frac{l}{5} – frac{5 m}{8} + frac{n}{16} – frac{9 o}{16} – frac{3 p}{16} – frac{7 q}{32} + frac{r}{32} + frac{17 x}{32} – frac{y}{8} + frac{4047}{128}$$
=
31.6171875 + 0.03125*r + 0.0625*n + 0.25*h + 0.625*g + 0.53125*x + 0.153125*k + 0.30625*f – 0.125*y – 0.1875*p – 0.625*m – 0.21875*q – 0.5625*o – 0.2*l
$$d_{1} = frac{5 f}{16} + frac{5 g}{4} + frac{h}{2} – frac{75 k}{32} – frac{5 m}{4} – frac{15 n}{8} + frac{15 o}{8} + frac{5 p}{8} – frac{15 q}{16} + frac{25 r}{16} + frac{25 x}{16} + frac{15 y}{4} – frac{4297}{64}$$
=
$$frac{5 f}{16} + frac{5 g}{4} + frac{h}{2} – frac{75 k}{32} – frac{5 m}{4} – frac{15 n}{8} + frac{15 o}{8} + frac{5 p}{8} – frac{15 q}{16} + frac{25 r}{16} + frac{25 x}{16} + frac{15 y}{4} – frac{4297}{64}$$
=
-67.140625 + 0.5*h + 0.3125*f + 0.625*p + 1.25*g + 1.875*o + 3.75*y + 1.5625*r + 1.5625*x – 1.25*m – 0.9375*q – 1.875*n – 2.34375*k
$$0 v + 0 u + 0 t + 0 s + 1200 r + 2500 q + 1200 p + 2500 o + 3500 n + 3600 m + 4000 l + 2500 k + 4500 x + 2800 y + 2700 h + 7800 g + 1500 f + 2300 d + 3800 c + 6700 a + 3000 b + 0 e = 1040930$$
$$0 v + 0 u + 0 t + 0 s + 1500 r + 500 q + 1000 p + 2000 o + 2000 n + 1000 m + 2800 l + 450 k + 2500 x + 3000 y + 1000 h + 3000 g + 900 f + 1000 d + 2000 c + 5000 a + 2000 b + 0 e = 582925$$
$$0 v + 0 u + 0 t + 0 s + 1000 r + 1000 q + 1000 p + 2000 o + 2500 n + 2000 m + 3000 l + 1000 k + 1500 x + 2000 y + 600 h + 2000 g + 500 f + 1300 d + 2000 c + 6000 a + 2000 b + 0 e = 594400$$
$$0 v + 0 u + 0 t + 0 s + 1500 r + 1000 q + 1000 p + 1500 o + 4000 n + 1500 m + 4000 l + 2000 k + 3500 x + 2500 y + 1500 h + 4500 g + 1500 f + 2000 d + 3000 c + 6500 a + 3000 b + 0 e = 809200$$
Приведём систему ур-ний к каноническому виду
$$6700 a + 3000 b + 3800 c + 2300 d + 1500 f + 7800 g + 2700 h + 2500 k + 4000 l + 3600 m + 3500 n + 2500 o + 1200 p + 2500 q + 1200 r + 4500 x + 2800 y = 1040930$$
$$5000 a + 2000 b + 2000 c + 1000 d + 900 f + 3000 g + 1000 h + 450 k + 2800 l + 1000 m + 2000 n + 2000 o + 1000 p + 500 q + 1500 r + 2500 x + 3000 y = 582925$$
$$6000 a + 2000 b + 2000 c + 1300 d + 500 f + 2000 g + 600 h + 1000 k + 3000 l + 2000 m + 2500 n + 2000 o + 1000 p + 1000 q + 1000 r + 1500 x + 2000 y = 594400$$
$$6500 a + 3000 b + 3000 c + 2000 d + 1500 f + 4500 g + 1500 h + 2000 k + 4000 l + 1500 m + 4000 n + 1500 o + 1000 p + 1000 q + 1500 r + 3500 x + 2500 y = 809200$$
Запишем систему линейных ур-ний в матричном виде
$$left[begin{array}{cccccccccccccccccc}6700 & 3000 & 3800 & 2300 & 1500 & 7800 & 2700 & 2500 & 4000 & 3600 & 3500 & 2500 & 1200 & 2500 & 1200 & 4500 & 2800 & 10409305000 & 2000 & 2000 & 1000 & 900 & 3000 & 1000 & 450 & 2800 & 1000 & 2000 & 2000 & 1000 & 500 & 1500 & 2500 & 3000 & 5829256000 & 2000 & 2000 & 1300 & 500 & 2000 & 600 & 1000 & 3000 & 2000 & 2500 & 2000 & 1000 & 1000 & 1000 & 1500 & 2000 & 5944006500 & 3000 & 3000 & 2000 & 1500 & 4500 & 1500 & 2000 & 4000 & 1500 & 4000 & 1500 & 1000 & 1000 & 1500 & 3500 & 2500 & 809200end{array}right]$$
В 1 ом столбце
$$left[begin{matrix}6700500060006500end{matrix}right]$$
делаем так, чтобы все элементы, кроме
1 го элемента равнялись нулю.
– Для этого берём 1 ую строку
$$left[begin{array}{cccccccccccccccccc}6700 & 3000 & 3800 & 2300 & 1500 & 7800 & 2700 & 2500 & 4000 & 3600 & 3500 & 2500 & 1200 & 2500 & 1200 & 4500 & 2800 & 1040930end{array}right]$$
,
и будем вычитать ее из других строк:
Из 2 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}0 & – frac{150000}{67} + 2000 & – frac{190000}{67} + 2000 & – frac{115000}{67} + 1000 & – frac{75000}{67} + 900 & – frac{390000}{67} + 3000 & – frac{135000}{67} + 1000 & – frac{125000}{67} + 450 & – frac{200000}{67} + 2800 & – frac{180000}{67} + 1000 & – frac{175000}{67} + 2000 & – frac{125000}{67} + 2000 & – frac{60000}{67} + 1000 & – frac{125000}{67} + 500 & – frac{60000}{67} + 1500 & – frac{225000}{67} + 2500 & – frac{140000}{67} + 3000 & – frac{52046500}{67} + 582925end{array}right] = left[begin{array}{cccccccccccccccccc}0 & – frac{16000}{67} & – frac{56000}{67} & – frac{48000}{67} & – frac{14700}{67} & – frac{189000}{67} & – frac{68000}{67} & – frac{94850}{67} & – frac{12400}{67} & – frac{113000}{67} & – frac{41000}{67} & frac{9000}{67} & frac{7000}{67} & – frac{91500}{67} & frac{40500}{67} & – frac{57500}{67} & frac{61000}{67} & – frac{12990525}{67}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 3000 & 3800 & 2300 & 1500 & 7800 & 2700 & 2500 & 4000 & 3600 & 3500 & 2500 & 1200 & 2500 & 1200 & 4500 & 2800 & 1040930 & – frac{16000}{67} & – frac{56000}{67} & – frac{48000}{67} & – frac{14700}{67} & – frac{189000}{67} & – frac{68000}{67} & – frac{94850}{67} & – frac{12400}{67} & – frac{113000}{67} & – frac{41000}{67} & frac{9000}{67} & frac{7000}{67} & – frac{91500}{67} & frac{40500}{67} & – frac{57500}{67} & frac{61000}{67} & – frac{12990525}{67}6000 & 2000 & 2000 & 1300 & 500 & 2000 & 600 & 1000 & 3000 & 2000 & 2500 & 2000 & 1000 & 1000 & 1000 & 1500 & 2000 & 5944006500 & 3000 & 3000 & 2000 & 1500 & 4500 & 1500 & 2000 & 4000 & 1500 & 4000 & 1500 & 1000 & 1000 & 1500 & 3500 & 2500 & 809200end{array}right]$$
Из 3 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}0 & – frac{180000}{67} + 2000 & – frac{228000}{67} + 2000 & – frac{138000}{67} + 1300 & – frac{90000}{67} + 500 & – frac{468000}{67} + 2000 & – frac{162000}{67} + 600 & – frac{150000}{67} + 1000 & – frac{240000}{67} + 3000 & – frac{216000}{67} + 2000 & – frac{210000}{67} + 2500 & – frac{150000}{67} + 2000 & – frac{72000}{67} + 1000 & – frac{150000}{67} + 1000 & – frac{72000}{67} + 1000 & – frac{270000}{67} + 1500 & – frac{168000}{67} + 2000 & – frac{62455800}{67} + 594400end{array}right] = left[begin{array}{cccccccccccccccccc}0 & – frac{46000}{67} & – frac{94000}{67} & – frac{50900}{67} & – frac{56500}{67} & – frac{334000}{67} & – frac{121800}{67} & – frac{83000}{67} & – frac{39000}{67} & – frac{82000}{67} & – frac{42500}{67} & – frac{16000}{67} & – frac{5000}{67} & – frac{83000}{67} & – frac{5000}{67} & – frac{169500}{67} & – frac{34000}{67} & – frac{22631000}{67}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 3000 & 3800 & 2300 & 1500 & 7800 & 2700 & 2500 & 4000 & 3600 & 3500 & 2500 & 1200 & 2500 & 1200 & 4500 & 2800 & 1040930 & – frac{16000}{67} & – frac{56000}{67} & – frac{48000}{67} & – frac{14700}{67} & – frac{189000}{67} & – frac{68000}{67} & – frac{94850}{67} & – frac{12400}{67} & – frac{113000}{67} & – frac{41000}{67} & frac{9000}{67} & frac{7000}{67} & – frac{91500}{67} & frac{40500}{67} & – frac{57500}{67} & frac{61000}{67} & – frac{12990525}{67} & – frac{46000}{67} & – frac{94000}{67} & – frac{50900}{67} & – frac{56500}{67} & – frac{334000}{67} & – frac{121800}{67} & – frac{83000}{67} & – frac{39000}{67} & – frac{82000}{67} & – frac{42500}{67} & – frac{16000}{67} & – frac{5000}{67} & – frac{83000}{67} & – frac{5000}{67} & – frac{169500}{67} & – frac{34000}{67} & – frac{22631000}{67}6500 & 3000 & 3000 & 2000 & 1500 & 4500 & 1500 & 2000 & 4000 & 1500 & 4000 & 1500 & 1000 & 1000 & 1500 & 3500 & 2500 & 809200end{array}right]$$
Из 4 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}0 & – frac{195000}{67} + 3000 & – frac{247000}{67} + 3000 & – frac{149500}{67} + 2000 & – frac{97500}{67} + 1500 & – frac{507000}{67} + 4500 & – frac{175500}{67} + 1500 & – frac{162500}{67} + 2000 & – frac{260000}{67} + 4000 & – frac{234000}{67} + 1500 & – frac{227500}{67} + 4000 & – frac{162500}{67} + 1500 & – frac{78000}{67} + 1000 & – frac{162500}{67} + 1000 & – frac{78000}{67} + 1500 & – frac{292500}{67} + 3500 & – frac{182000}{67} + 2500 & – frac{67660450}{67} + 809200end{array}right] = left[begin{array}{cccccccccccccccccc}0 & frac{6000}{67} & – frac{46000}{67} & – frac{15500}{67} & frac{3000}{67} & – frac{205500}{67} & – frac{75000}{67} & – frac{28500}{67} & frac{8000}{67} & – frac{133500}{67} & frac{40500}{67} & – frac{62000}{67} & – frac{11000}{67} & – frac{95500}{67} & frac{22500}{67} & – frac{58000}{67} & – frac{14500}{67} & – frac{13444050}{67}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 3000 & 3800 & 2300 & 1500 & 7800 & 2700 & 2500 & 4000 & 3600 & 3500 & 2500 & 1200 & 2500 & 1200 & 4500 & 2800 & 1040930 & – frac{16000}{67} & – frac{56000}{67} & – frac{48000}{67} & – frac{14700}{67} & – frac{189000}{67} & – frac{68000}{67} & – frac{94850}{67} & – frac{12400}{67} & – frac{113000}{67} & – frac{41000}{67} & frac{9000}{67} & frac{7000}{67} & – frac{91500}{67} & frac{40500}{67} & – fr
ac{57500}{67} & frac{61000}{67} & – frac{12990525}{67} & – frac{46000}{67} & – frac{94000}{67} & – frac{50900}{67} & – frac{56500}{67} & – frac{334000}{67} & – frac{121800}{67} & – frac{83000}{67} & – frac{39000}{67} & – frac{82000}{67} & – frac{42500}{67} & – frac{16000}{67} & – frac{5000}{67} & – frac{83000}{67} & – frac{5000}{67} & – frac{169500}{67} & – frac{34000}{67} & – frac{22631000}{67} & frac{6000}{67} & – frac{46000}{67} & – frac{15500}{67} & frac{3000}{67} & – frac{205500}{67} & – frac{75000}{67} & – frac{28500}{67} & frac{8000}{67} & – frac{133500}{67} & frac{40500}{67} & – frac{62000}{67} & – frac{11000}{67} & – frac{95500}{67} & frac{22500}{67} & – frac{58000}{67} & – frac{14500}{67} & – frac{13444050}{67}end{array}right]$$
Во 2 ом столбце
$$left[begin{matrix}3000 – frac{16000}{67} – frac{46000}{67}\frac{6000}{67}end{matrix}right]$$
делаем так, чтобы все элементы, кроме
2 го элемента равнялись нулю.
– Для этого берём 2 ую строку
$$left[begin{array}{cccccccccccccccccc}0 & – frac{16000}{67} & – frac{56000}{67} & – frac{48000}{67} & – frac{14700}{67} & – frac{189000}{67} & – frac{68000}{67} & – frac{94850}{67} & – frac{12400}{67} & – frac{113000}{67} & – frac{41000}{67} & frac{9000}{67} & frac{7000}{67} & – frac{91500}{67} & frac{40500}{67} & – frac{57500}{67} & frac{61000}{67} & – frac{12990525}{67}end{array}right]$$
,
и будем вычитать ее из других строк:
Из 1 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & -6700 & -6700 & – frac{11025}{4} + 1500 & – frac{70875}{2} + 7800 & -10050 & – frac{142275}{8} + 2500 & 1675 & – frac{42375}{2} + 3600 & – frac{15375}{2} + 3500 & – frac{-3375}{2} + 2500 & 1200 – – frac{2625}{2} & – frac{68625}{4} + 2500 & 1200 – – frac{30375}{4} & – frac{43125}{4} + 4500 & 2800 – – frac{22875}{2} & – frac{38971575}{16} + 1040930end{array}right] = left[begin{array}{cccccccccccccccccc}6700 & 0 & -6700 & -6700 & – frac{5025}{4} & – frac{55275}{2} & -10050 & – frac{122275}{8} & 1675 & – frac{35175}{2} & – frac{8375}{2} & frac{8375}{2} & frac{5025}{2} & – frac{58625}{4} & frac{35175}{4} & – frac{25125}{4} & frac{28475}{2} & – frac{22316695}{16}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & -6700 & -6700 & – frac{5025}{4} & – frac{55275}{2} & -10050 & – frac{122275}{8} & 1675 & – frac{35175}{2} & – frac{8375}{2} & frac{8375}{2} & frac{5025}{2} & – frac{58625}{4} & frac{35175}{4} & – frac{25125}{4} & frac{28475}{2} & – frac{22316695}{16} & – frac{16000}{67} & – frac{56000}{67} & – frac{48000}{67} & – frac{14700}{67} & – frac{189000}{67} & – frac{68000}{67} & – frac{94850}{67} & – frac{12400}{67} & – frac{113000}{67} & – frac{41000}{67} & frac{9000}{67} & frac{7000}{67} & – frac{91500}{67} & frac{40500}{67} & – frac{57500}{67} & frac{61000}{67} & – frac{12990525}{67} & – frac{46000}{67} & – frac{94000}{67} & – frac{50900}{67} & – frac{56500}{67} & – frac{334000}{67} & – frac{121800}{67} & – frac{83000}{67} & – frac{39000}{67} & – frac{82000}{67} & – frac{42500}{67} & – frac{16000}{67} & – frac{5000}{67} & – frac{83000}{67} & – frac{5000}{67} & – frac{169500}{67} & – frac{34000}{67} & – frac{22631000}{67} & frac{6000}{67} & – frac{46000}{67} & – frac{15500}{67} & frac{3000}{67} & – frac{205500}{67} & – frac{75000}{67} & – frac{28500}{67} & frac{8000}{67} & – frac{133500}{67} & frac{40500}{67} & – frac{62000}{67} & – frac{11000}{67} & – frac{95500}{67} & frac{22500}{67} & – frac{58000}{67} & – frac{14500}{67} & – frac{13444050}{67}end{array}right]$$
Из 3 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}0 & – frac{46000}{67} – – frac{46000}{67} & – frac{94000}{67} – – frac{161000}{67} & – frac{50900}{67} – – frac{138000}{67} & – frac{56500}{67} – – frac{84525}{134} & – frac{334000}{67} – – frac{543375}{67} & – frac{121800}{67} – – frac{195500}{67} & – frac{83000}{67} – – frac{1090775}{268} & – frac{39000}{67} – – frac{35650}{67} & – frac{82000}{67} – – frac{324875}{67} & – frac{42500}{67} – – frac{117875}{67} & – frac{25875}{67} – frac{16000}{67} & – frac{20125}{67} – frac{5000}{67} & – frac{83000}{67} – – frac{526125}{134} & – frac{232875}{134} – frac{5000}{67} & – frac{169500}{67} – – frac{330625}{134} & – frac{175375}{67} – frac{34000}{67} & – frac{22631000}{67} – – frac{298782075}{536}end{array}right] = left[begin{array}{cccccccccccccccccc}0 & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & -6700 & -6700 & – frac{5025}{4} & – frac{55275}{2} & -10050 & – frac{122275}{8} & 1675 & – frac{35175}{2} & – frac{8375}{2} & frac{8375}{2} & frac{5025}{2} & – frac{58625}{4} & frac{35175}{4} & – frac{25125}{4} & frac{28475}{2} & – frac{22316695}{16} & – frac{16000}{67} & – frac{56000}{67} & – frac{48000}{67} & – frac{14700}{67} & – frac{189000}{67} & – frac{68000}{67} & – frac{94850}{67} & – frac{12400}{67} & – frac{113000}{67} & – frac{41000}{67} & frac{9000}{67} & frac{7000}{67} & – frac{91500}{67} & frac{40500}{67} & – frac{57500}{67} & frac{61000}{67} & – frac{12990525}{67} & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8} & frac{6000}{67} & – frac{46000}{67} & – frac{15500}{67} & frac{3000}{67} & – frac{205500}{67} & – frac{75000}{67} & – frac{28500}{67} & frac{8000}{67} & – frac{133500}{67} & frac{40500}{67} & – frac{62000}{67} & – frac{11000}{67} & – frac{95500}{67} & frac{22500}{67} & – frac{58000}{67} & – frac{14500}{67} & – frac{13444050}{67}end{array}right]$$
Из 4 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}0 & – frac{6000}{67} + frac{6000}{67} & – frac{46000}{67} – frac{21000}{67} & – frac{18000}{67} – frac{15500}{67} & – frac{11025}{134} + frac{3000}{67} & – frac{205500}{67} – frac{70875}{67} & – frac{75000}{67} – frac{25500}{67} & – frac{142275}{268} – frac{28500}{67} & – frac{4650}{67} + frac{8000}{67} & – frac{133500}{67} – frac{42375}{67} & – frac{15375}{67} + frac{40500}{67} & – frac{62000}{67} – – frac{3375}{67} & – frac{11000}{67} – – frac{2625}{67} & – frac{95500}{67} – frac{68625}{134} & – frac{-30375}{134} + frac{22500}{67} & – frac{58000}{67} – frac{43125}{134} & – frac{14500}{67} – – frac{22875}{67} & – frac{13444050}{67} – frac{38971575}{536}end{array}right] = left[begin{array}{cccccccccccccccccc}0 & 0 & -1000 & -500 & – frac{75}{2} & -4125 & -1500 & – frac{3825}{4} & 50 & -2625 & 375 & -875 & -125 & – frac{3875}{2} & frac{1125}{2} & – frac{2375}{2} & 125 & – frac{2186925}{8}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & -6700 & -6700 & – frac{5025}{4} & – frac{55275}{2} & -10050 & – frac{122275}{8} & 1675 & – frac{35175}{2} & – frac{8375}{2} & frac{8375}{2} & frac{5025}{2} & – frac{58625}{4} & frac{35175}{4} & – frac{25125}{4} & frac{28475}{2} & – frac{22316695}{16} & – frac{16000}{67} & – frac{56000}{67} & – frac{48000}{67} & – frac{14700}{67} & – frac{189000}{67} & – frac{68000}{67} & – frac{94850}{67} & – frac{12400}{67} & – frac{113000}{67} & – frac{41000}{67} & frac{9000}{67} & frac{7000}{67} & – frac{91500}{67} & frac{40500}{67} & – frac{57500}{67} & frac{61000}{67} & – frac{12990525}{67} & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8} & 0 & -1000 & -500 & – frac{75}{2} & -4125 & -1500 & – frac{3825}{4} & 50 & -2625 & 375 & -875 &
-125 & – frac{3875}{2} & frac{1125}{2} & – frac{2375}{2} & 125 & – frac{2186925}{8}end{array}right]$$
В 3 ом столбце
$$left[begin{matrix}-6700 – frac{56000}{67}1000 -1000end{matrix}right]$$
делаем так, чтобы все элементы, кроме
3 го элемента равнялись нулю.
– Для этого берём 3 ую строку
$$left[begin{array}{cccccccccccccccccc}0 & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8}end{array}right]$$
,
и будем вычитать ее из других строк:
Из 1 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & – frac{5695}{4} – frac{5025}{4} & – frac{55275}{2} – – frac{41875}{2} & -2680 & – frac{122275}{8} – – frac{151755}{8} & 1340 & – frac{35175}{2} – – frac{48575}{2} & – frac{8375}{2} – – frac{15075}{2} & – frac{8375}{2} + frac{8375}{2} & – frac{5025}{2} + frac{5025}{2} & – frac{58625}{4} – – frac{72025}{4} & – frac{48575}{4} + frac{35175}{4} & – frac{25125}{4} – frac{1675}{4} & – frac{41875}{2} + frac{28475}{2} & – frac{22316695}{16} – – frac{23546815}{16}end{array}right] = left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} & – frac{16000}{67} & – frac{56000}{67} & – frac{48000}{67} & – frac{14700}{67} & – frac{189000}{67} & – frac{68000}{67} & – frac{94850}{67} & – frac{12400}{67} & – frac{113000}{67} & – frac{41000}{67} & frac{9000}{67} & frac{7000}{67} & – frac{91500}{67} & frac{40500}{67} & – frac{57500}{67} & frac{61000}{67} & – frac{12990525}{67} & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8} & 0 & -1000 & -500 & – frac{75}{2} & -4125 & -1500 & – frac{3825}{4} & 50 & -2625 & 375 & -875 & -125 & – frac{3875}{2} & frac{1125}{2} & – frac{2375}{2} & 125 & – frac{2186925}{8}end{array}right]$$
Из 2 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}0 & – frac{16000}{67} & – frac{56000}{67} – – frac{56000}{67} & – frac{48000}{67} – – frac{72800}{67} & – frac{14700}{67} – frac{11900}{67} & – frac{189000}{67} – – frac{175000}{67} & – frac{68000}{67} – – frac{61600}{67} & – frac{94850}{67} – – frac{158550}{67} & – frac{12400}{67} – frac{2800}{67} & – frac{113000}{67} – – frac{203000}{67} & – frac{41000}{67} – – frac{63000}{67} & – frac{35000}{67} + frac{9000}{67} & – frac{21000}{67} + frac{7000}{67} & – frac{91500}{67} – – frac{150500}{67} & – frac{101500}{67} + frac{40500}{67} & – frac{57500}{67} – frac{3500}{67} & – frac{175000}{67} + frac{61000}{67} & – frac{12990525}{67} – – frac{12300575}{67}end{array}right] = left[begin{array}{cccccccccccccccccc}0 & – frac{16000}{67} & 0 & frac{24800}{67} & – frac{26600}{67} & – frac{14000}{67} & – frac{6400}{67} & frac{63700}{67} & – frac{15200}{67} & frac{90000}{67} & frac{22000}{67} & – frac{26000}{67} & – frac{14000}{67} & frac{59000}{67} & – frac{61000}{67} & – frac{61000}{67} & – frac{114000}{67} & – frac{689950}{67}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} & – frac{16000}{67} & 0 & frac{24800}{67} & – frac{26600}{67} & – frac{14000}{67} & – frac{6400}{67} & frac{63700}{67} & – frac{15200}{67} & frac{90000}{67} & frac{22000}{67} & – frac{26000}{67} & – frac{14000}{67} & frac{59000}{67} & – frac{61000}{67} & – frac{61000}{67} & – frac{114000}{67} & – frac{689950}{67} & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8} & 0 & -1000 & -500 & – frac{75}{2} & -4125 & -1500 & – frac{3825}{4} & 50 & -2625 & 375 & -875 & -125 & – frac{3875}{2} & frac{1125}{2} & – frac{2375}{2} & 125 & – frac{2186925}{8}end{array}right]$$
Из 4 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}0 & 0 & 0 & 800 & – frac{425}{2} – frac{75}{2} & -1000 & -400 & – frac{3825}{4} – – frac{11325}{4} & 0 & 1000 & 1500 & -1500 & -500 & – frac{3875}{2} – – frac{5375}{2} & – frac{3625}{2} + frac{1125}{2} & – frac{2375}{2} – frac{125}{2} & -3000 & – frac{2186925}{8} – – frac{1757225}{8}end{array}right] = left[begin{array}{cccccccccccccccccc}0 & 0 & 0 & 800 & -250 & -1000 & -400 & 1875 & 0 & 1000 & 1500 & -1500 & -500 & 750 & -1250 & -1250 & -3000 & – frac{107425}{2}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} & – frac{16000}{67} & 0 & frac{24800}{67} & – frac{26600}{67} & – frac{14000}{67} & – frac{6400}{67} & frac{63700}{67} & – frac{15200}{67} & frac{90000}{67} & frac{22000}{67} & – frac{26000}{67} & – frac{14000}{67} & frac{59000}{67} & – frac{61000}{67} & – frac{61000}{67} & – frac{114000}{67} & – frac{689950}{67} & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8} & 0 & 0 & 800 & -250 & -1000 & -400 & 1875 & 0 & 1000 & 1500 & -1500 & -500 & 750 & -1250 & -1250 & -3000 & – frac{107425}{2}end{array}right]$$
В 4 ом столбце
$$left[begin{matrix}2010\frac{24800}{67}1300800end{matrix}right]$$
делаем так, чтобы все элементы, кроме
1 го элемента равнялись нулю.
– Для этого берём 1 ую строку
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2}end{array}right]$$
,
и будем вычитать ее из других строк:
Из 2 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}- frac{248000}{201} & – frac{16000}{67} & 0 & – frac{24800}{67} + frac{24800}{67} & – frac{26600}{67} – – frac{99200}{201} & – frac{14000}{67} – – frac{248000}{201} & – frac{6400}{67} – – frac{99200}{201} & – frac{136400}{201} + frac{63700}{67} & – frac{49600}{201} – frac{15200}{67} & – frac{248000}{201} + frac{90000}{67} & – frac{124000}{201} + frac{22000}{67} & – frac{26000}{67} & – frac{14000}{67} & – frac{124000}{201} + frac{59000}{67} & – frac{61000}{67} – – frac{124000}{201} & – frac{61000}{67} – – frac{248000}{201} & – frac{114000}{67} – – frac{248000}{201} & – frac{948600}{67} – frac{689950}{67}end{array}right] = left[begin{array}{cccccccccccccccccc}- frac{248000}{201} & – frac{16000}{67} & 0 & 0 & frac{19400}{201} & frac{206000}{201} & frac{80000}{201} & frac{54700}{201} & – frac{95200}{201} & frac{22000}{201} & – frac{58000}{201} & – frac{26000}{67} & – frac{14000}{67} & frac{53000}{201} & – frac{59000}{201} & frac{65000}{201} & – frac{94000}{201} & – frac{1638550}{67}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} – frac{248000}{201} & – frac{16000}{67} & 0 & 0 & frac{19400}{201} & frac{206000}{201} & frac{80000}{201} & frac{54700}{201} & – frac{95200}{201} & frac{22000}{201} & – frac{58000}{201} & – frac{26000}{67} & – frac{14000}{67} & frac{53000}{201} & – frac{59000}{2
01} & frac{65000}{201} & – frac{94000}{201} & – frac{1638550}{67} & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8} & 0 & 0 & 800 & -250 & -1000 & -400 & 1875 & 0 & 1000 & 1500 & -1500 & -500 & 750 & -1250 & -1250 & -3000 & – frac{107425}{2}end{array}right]$$
Из 3 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}- frac{13000}{3} & 0 & 1000 & 0 & – frac{425}{2} – – frac{5200}{3} & 3125 – – frac{13000}{3} & 1100 – – frac{5200}{3} & – frac{7150}{3} + frac{11325}{4} & – frac{2600}{3} – 50 & – frac{13000}{3} + 3625 & – frac{6500}{3} + 1125 & -625 & -375 & – frac{6500}{3} + frac{5375}{2} & – frac{3625}{2} – – frac{6500}{3} & – frac{125}{2} – – frac{13000}{3} & -3125 – – frac{13000}{3} & frac{1359425}{8}end{array}right] = left[begin{array}{cccccccccccccccccc}- frac{13000}{3} & 0 & 1000 & 0 & frac{9125}{6} & frac{22375}{3} & frac{8500}{3} & frac{5375}{12} & – frac{2750}{3} & – frac{2125}{3} & – frac{3125}{3} & -625 & -375 & frac{3125}{6} & frac{2125}{6} & frac{25625}{6} & frac{3625}{3} & frac{1359425}{8}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} – frac{248000}{201} & – frac{16000}{67} & 0 & 0 & frac{19400}{201} & frac{206000}{201} & frac{80000}{201} & frac{54700}{201} & – frac{95200}{201} & frac{22000}{201} & – frac{58000}{201} & – frac{26000}{67} & – frac{14000}{67} & frac{53000}{201} & – frac{59000}{201} & frac{65000}{201} & – frac{94000}{201} & – frac{1638550}{67} – frac{13000}{3} & 0 & 1000 & 0 & frac{9125}{6} & frac{22375}{3} & frac{8500}{3} & frac{5375}{12} & – frac{2750}{3} & – frac{2125}{3} & – frac{3125}{3} & -625 & -375 & frac{3125}{6} & frac{2125}{6} & frac{25625}{6} & frac{3625}{3} & frac{1359425}{8} & 0 & 0 & 800 & -250 & -1000 & -400 & 1875 & 0 & 1000 & 1500 & -1500 & -500 & 750 & -1250 & -1250 & -3000 & – frac{107425}{2}end{array}right]$$
Из 4 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}- frac{8000}{3} & 0 & 0 & 0 & -250 – – frac{3200}{3} & -1000 – – frac{8000}{3} & -400 – – frac{3200}{3} & – frac{4400}{3} + 1875 & – frac{1600}{3} & – frac{8000}{3} + 1000 & – frac{4000}{3} + 1500 & -1500 & -500 & – frac{4000}{3} + 750 & -1250 – – frac{4000}{3} & -1250 – – frac{8000}{3} & -3000 – – frac{8000}{3} & – frac{168625}{2}end{array}right] = left[begin{array}{cccccccccccccccccc}- frac{8000}{3} & 0 & 0 & 0 & frac{2450}{3} & frac{5000}{3} & frac{2000}{3} & frac{1225}{3} & – frac{1600}{3} & – frac{5000}{3} & frac{500}{3} & -1500 & -500 & – frac{1750}{3} & frac{250}{3} & frac{4250}{3} & – frac{1000}{3} & – frac{168625}{2}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} – frac{248000}{201} & – frac{16000}{67} & 0 & 0 & frac{19400}{201} & frac{206000}{201} & frac{80000}{201} & frac{54700}{201} & – frac{95200}{201} & frac{22000}{201} & – frac{58000}{201} & – frac{26000}{67} & – frac{14000}{67} & frac{53000}{201} & – frac{59000}{201} & frac{65000}{201} & – frac{94000}{201} & – frac{1638550}{67} – frac{13000}{3} & 0 & 1000 & 0 & frac{9125}{6} & frac{22375}{3} & frac{8500}{3} & frac{5375}{12} & – frac{2750}{3} & – frac{2125}{3} & – frac{3125}{3} & -625 & -375 & frac{3125}{6} & frac{2125}{6} & frac{25625}{6} & frac{3625}{3} & frac{1359425}{8} – frac{8000}{3} & 0 & 0 & 0 & frac{2450}{3} & frac{5000}{3} & frac{2000}{3} & frac{1225}{3} & – frac{1600}{3} & – frac{5000}{3} & frac{500}{3} & -1500 & -500 & – frac{1750}{3} & frac{250}{3} & frac{4250}{3} & – frac{1000}{3} & – frac{168625}{2}end{array}right]$$
В 1 ом столбце
$$left[begin{matrix}6700 – frac{248000}{201} – frac{13000}{3} – frac{8000}{3}end{matrix}right]$$
делаем так, чтобы все элементы, кроме
1 го элемента равнялись нулю.
– Для этого берём 1 ую строку
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2}end{array}right]$$
,
и будем вычитать ее из других строк:
Из 2 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}- frac{248000}{201} – – frac{248000}{201} & – frac{16000}{67} & 0 & – frac{-24800}{67} & – frac{99200}{201} + frac{19400}{201} & – frac{248000}{201} + frac{206000}{201} & – frac{99200}{201} + frac{80000}{201} & frac{54700}{201} – – frac{136400}{201} & – frac{95200}{201} – – frac{49600}{201} & frac{22000}{201} – – frac{248000}{201} & – frac{58000}{201} – – frac{124000}{201} & – frac{26000}{67} & – frac{14000}{67} & frac{53000}{201} – – frac{124000}{201} & – frac{124000}{201} – frac{59000}{201} & – frac{248000}{201} + frac{65000}{201} & – frac{248000}{201} – frac{94000}{201} & – frac{1638550}{67} – – frac{948600}{67}end{array}right] = left[begin{array}{cccccccccccccccccc}0 & – frac{16000}{67} & 0 & frac{24800}{67} & – frac{26600}{67} & – frac{14000}{67} & – frac{6400}{67} & frac{63700}{67} & – frac{15200}{67} & frac{90000}{67} & frac{22000}{67} & – frac{26000}{67} & – frac{14000}{67} & frac{59000}{67} & – frac{61000}{67} & – frac{61000}{67} & – frac{114000}{67} & – frac{689950}{67}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} & – frac{16000}{67} & 0 & frac{24800}{67} & – frac{26600}{67} & – frac{14000}{67} & – frac{6400}{67} & frac{63700}{67} & – frac{15200}{67} & frac{90000}{67} & frac{22000}{67} & – frac{26000}{67} & – frac{14000}{67} & frac{59000}{67} & – frac{61000}{67} & – frac{61000}{67} & – frac{114000}{67} & – frac{689950}{67} – frac{13000}{3} & 0 & 1000 & 0 & frac{9125}{6} & frac{22375}{3} & frac{8500}{3} & frac{5375}{12} & – frac{2750}{3} & – frac{2125}{3} & – frac{3125}{3} & -625 & -375 & frac{3125}{6} & frac{2125}{6} & frac{25625}{6} & frac{3625}{3} & frac{1359425}{8} – frac{8000}{3} & 0 & 0 & 0 & frac{2450}{3} & frac{5000}{3} & frac{2000}{3} & frac{1225}{3} & – frac{1600}{3} & – frac{5000}{3} & frac{500}{3} & -1500 & -500 & – frac{1750}{3} & frac{250}{3} & frac{4250}{3} & – frac{1000}{3} & – frac{168625}{2}end{array}right]$$
Из 3 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}- frac{13000}{3} – – frac{13000}{3} & 0 & 1000 & 1300 & – frac{5200}{3} + frac{9125}{6} & – frac{13000}{3} + frac{22375}{3} & – frac{5200}{3} + frac{8500}{3} & frac{5375}{12} – – frac{7150}{3} & – frac{2750}{3} – – frac{2600}{3} & – frac{2125}{3} – – frac{13000}{3} & – frac{3125}{3} – – frac{6500}{3} & -625 & -375 & frac{3125}{6} – – frac{6500}{3} & – frac{6500}{3} + frac{2125}{6} & – frac{13000}{3} + frac{25625}{6} & – frac{13000}{3} + frac{3625}{3} & frac{1757225}{8}end{array}right] = left[begin{array}{cccccccccccccccccc}0 & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} & – frac{16000}{67} & 0 & frac{24800}{67} & – frac{26600}{67} & – frac{14000}{67} & – frac{6400}{67} & frac{63700}{67} & – frac{15200}{67} & frac{90000}{67} & frac{22000}{67} & – frac{26000}{67} & – frac{14000}{67} & frac{59000}{67} & – frac{61000}{67} & – frac{61000}{67} & – frac{11400
0}{67} & – frac{689950}{67} & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8} – frac{8000}{3} & 0 & 0 & 0 & frac{2450}{3} & frac{5000}{3} & frac{2000}{3} & frac{1225}{3} & – frac{1600}{3} & – frac{5000}{3} & frac{500}{3} & -1500 & -500 & – frac{1750}{3} & frac{250}{3} & frac{4250}{3} & – frac{1000}{3} & – frac{168625}{2}end{array}right]$$
Из 4 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}- frac{8000}{3} – – frac{8000}{3} & 0 & 0 & 800 & – frac{3200}{3} + frac{2450}{3} & – frac{8000}{3} + frac{5000}{3} & – frac{3200}{3} + frac{2000}{3} & frac{1225}{3} – – frac{4400}{3} & – frac{1600}{3} – – frac{1600}{3} & – frac{5000}{3} – – frac{8000}{3} & frac{500}{3} – – frac{4000}{3} & -1500 & -500 & – frac{1750}{3} – – frac{4000}{3} & – frac{4000}{3} + frac{250}{3} & – frac{8000}{3} + frac{4250}{3} & – frac{8000}{3} – frac{1000}{3} & – frac{107425}{2}end{array}right] = left[begin{array}{cccccccccccccccccc}0 & 0 & 0 & 800 & -250 & -1000 & -400 & 1875 & 0 & 1000 & 1500 & -1500 & -500 & 750 & -1250 & -1250 & -3000 & – frac{107425}{2}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} & – frac{16000}{67} & 0 & frac{24800}{67} & – frac{26600}{67} & – frac{14000}{67} & – frac{6400}{67} & frac{63700}{67} & – frac{15200}{67} & frac{90000}{67} & frac{22000}{67} & – frac{26000}{67} & – frac{14000}{67} & frac{59000}{67} & – frac{61000}{67} & – frac{61000}{67} & – frac{114000}{67} & – frac{689950}{67} & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8} & 0 & 0 & 800 & -250 & -1000 & -400 & 1875 & 0 & 1000 & 1500 & -1500 & -500 & 750 & -1250 & -1250 & -3000 & – frac{107425}{2}end{array}right]$$
В 4 ом столбце
$$left[begin{matrix}2010\frac{24800}{67}1300800end{matrix}right]$$
делаем так, чтобы все элементы, кроме
1 го элемента равнялись нулю.
– Для этого берём 1 ую строку
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2}end{array}right]$$
,
и будем вычитать ее из других строк:
Из 2 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}- frac{248000}{201} & – frac{16000}{67} & 0 & – frac{24800}{67} + frac{24800}{67} & – frac{26600}{67} – – frac{99200}{201} & – frac{14000}{67} – – frac{248000}{201} & – frac{6400}{67} – – frac{99200}{201} & – frac{136400}{201} + frac{63700}{67} & – frac{49600}{201} – frac{15200}{67} & – frac{248000}{201} + frac{90000}{67} & – frac{124000}{201} + frac{22000}{67} & – frac{26000}{67} & – frac{14000}{67} & – frac{124000}{201} + frac{59000}{67} & – frac{61000}{67} – – frac{124000}{201} & – frac{61000}{67} – – frac{248000}{201} & – frac{114000}{67} – – frac{248000}{201} & – frac{948600}{67} – frac{689950}{67}end{array}right] = left[begin{array}{cccccccccccccccccc}- frac{248000}{201} & – frac{16000}{67} & 0 & 0 & frac{19400}{201} & frac{206000}{201} & frac{80000}{201} & frac{54700}{201} & – frac{95200}{201} & frac{22000}{201} & – frac{58000}{201} & – frac{26000}{67} & – frac{14000}{67} & frac{53000}{201} & – frac{59000}{201} & frac{65000}{201} & – frac{94000}{201} & – frac{1638550}{67}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} – frac{248000}{201} & – frac{16000}{67} & 0 & 0 & frac{19400}{201} & frac{206000}{201} & frac{80000}{201} & frac{54700}{201} & – frac{95200}{201} & frac{22000}{201} & – frac{58000}{201} & – frac{26000}{67} & – frac{14000}{67} & frac{53000}{201} & – frac{59000}{201} & frac{65000}{201} & – frac{94000}{201} & – frac{1638550}{67} & 0 & 1000 & 1300 & – frac{425}{2} & 3125 & 1100 & frac{11325}{4} & -50 & 3625 & 1125 & -625 & -375 & frac{5375}{2} & – frac{3625}{2} & – frac{125}{2} & -3125 & frac{1757225}{8} & 0 & 0 & 800 & -250 & -1000 & -400 & 1875 & 0 & 1000 & 1500 & -1500 & -500 & 750 & -1250 & -1250 & -3000 & – frac{107425}{2}end{array}right]$$
Из 3 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}- frac{13000}{3} & 0 & 1000 & 0 & – frac{425}{2} – – frac{5200}{3} & 3125 – – frac{13000}{3} & 1100 – – frac{5200}{3} & – frac{7150}{3} + frac{11325}{4} & – frac{2600}{3} – 50 & – frac{13000}{3} + 3625 & – frac{6500}{3} + 1125 & -625 & -375 & – frac{6500}{3} + frac{5375}{2} & – frac{3625}{2} – – frac{6500}{3} & – frac{125}{2} – – frac{13000}{3} & -3125 – – frac{13000}{3} & frac{1359425}{8}end{array}right] = left[begin{array}{cccccccccccccccccc}- frac{13000}{3} & 0 & 1000 & 0 & frac{9125}{6} & frac{22375}{3} & frac{8500}{3} & frac{5375}{12} & – frac{2750}{3} & – frac{2125}{3} & – frac{3125}{3} & -625 & -375 & frac{3125}{6} & frac{2125}{6} & frac{25625}{6} & frac{3625}{3} & frac{1359425}{8}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} – frac{248000}{201} & – frac{16000}{67} & 0 & 0 & frac{19400}{201} & frac{206000}{201} & frac{80000}{201} & frac{54700}{201} & – frac{95200}{201} & frac{22000}{201} & – frac{58000}{201} & – frac{26000}{67} & – frac{14000}{67} & frac{53000}{201} & – frac{59000}{201} & frac{65000}{201} & – frac{94000}{201} & – frac{1638550}{67} – frac{13000}{3} & 0 & 1000 & 0 & frac{9125}{6} & frac{22375}{3} & frac{8500}{3} & frac{5375}{12} & – frac{2750}{3} & – frac{2125}{3} & – frac{3125}{3} & -625 & -375 & frac{3125}{6} & frac{2125}{6} & frac{25625}{6} & frac{3625}{3} & frac{1359425}{8} & 0 & 0 & 800 & -250 & -1000 & -400 & 1875 & 0 & 1000 & 1500 & -1500 & -500 & 750 & -1250 & -1250 & -3000 & – frac{107425}{2}end{array}right]$$
Из 4 ой строки вычитаем:
$$left[begin{array}{cccccccccccccccccc}- frac{8000}{3} & 0 & 0 & 0 & -250 – – frac{3200}{3} & -1000 – – frac{8000}{3} & -400 – – frac{3200}{3} & – frac{4400}{3} + 1875 & – frac{1600}{3} & – frac{8000}{3} + 1000 & – frac{4000}{3} + 1500 & -1500 & -500 & – frac{4000}{3} + 750 & -1250 – – frac{4000}{3} & -1250 – – frac{8000}{3} & -3000 – – frac{8000}{3} & – frac{168625}{2}end{array}right] = left[begin{array}{cccccccccccccccccc}- frac{8000}{3} & 0 & 0 & 0 & frac{2450}{3} & frac{5000}{3} & frac{2000}{3} & frac{1225}{3} & – frac{1600}{3} & – frac{5000}{3} & frac{500}{3} & -1500 & -500 & – frac{1750}{3} & frac{250}{3} & frac{4250}{3} & – frac{1000}{3} & – frac{168625}{2}end{array}right]$$
получаем
$$left[begin{array}{cccccccccccccccccc}6700 & 0 & 0 & 2010 & -2680 & -6700 & -2680 & 3685 & 1340 & 6700 & 3350 & 0 & 0 & 3350 & -3350 & -6700 & -6700 & frac{153765}{2} – frac{248000}{201} & – frac{16000}{67} & 0 & 0 & frac{19400}{201} & frac{206000}{201} & frac{80000}{201} & frac{54700}{201} & – frac{95200}{201} & frac{22000}{201} & – frac{58000}{201} & – frac{26000}{67} & – frac{14000}{67} & frac{53000}{201} & – frac{59000}{201} & frac{65000}{201} & – frac{94000}{201} & – frac{1638550}{67} – frac{13000}{3} & 0 & 1000 & 0 & frac{9125}{6} & frac{22375}{3} & frac{8500}{3} & frac{5375}{12} & – frac{2750}{3} & – frac{2125}{3} & – frac{3125}{3} & -625 & -375 & frac{3125}{6} & frac{2125}{6} & frac{25625}{6} & frac{3625}{3} & frac{1359425}{8} – frac{8000}{3} & 0 & 0 & 0 & frac{2450}{3} & frac{5000}{3} & frac{2000}{3} & frac{1225}{3} & – frac{1600}{3} & – fra
c{5000}{3} & frac{500}{3} & -1500 & -500 & – frac{1750}{3} & frac{250}{3} & frac{4250}{3} & – frac{1000}{3} & – frac{168625}{2}end{array}right]$$
Все почти готово – осталось только найти неизвестные, решая элементарные ур-ния:
$$6700 x_{1} + 6700 x_{10} + 3350 x_{11} + 3350 x_{14} – 3350 x_{15} – 6700 x_{16} – 6700 x_{17} + 2010 x_{4} – 2680 x_{5} – 6700 x_{6} – 2680 x_{7} + 3685 x_{8} + 1340 x_{9} – frac{153765}{2} = 0$$
$$- frac{248000 x_{1}}{201} + frac{22000 x_{10}}{201} – frac{58000 x_{11}}{201} – frac{26000 x_{12}}{67} – frac{14000 x_{13}}{67} + frac{53000 x_{14}}{201} – frac{59000 x_{15}}{201} + frac{65000 x_{16}}{201} – frac{94000 x_{17}}{201} – frac{16000 x_{2}}{67} + frac{19400 x_{5}}{201} + frac{206000 x_{6}}{201} + frac{80000 x_{7}}{201} + frac{54700 x_{8}}{201} – frac{95200 x_{9}}{201} + frac{1638550}{67} = 0$$
$$- frac{13000 x_{1}}{3} – frac{2125 x_{10}}{3} – frac{3125 x_{11}}{3} – 625 x_{12} – 375 x_{13} + frac{3125 x_{14}}{6} + frac{2125 x_{15}}{6} + frac{25625 x_{16}}{6} + frac{3625 x_{17}}{3} + 1000 x_{3} + frac{9125 x_{5}}{6} + frac{22375 x_{6}}{3} + frac{8500 x_{7}}{3} + frac{5375 x_{8}}{12} – frac{2750 x_{9}}{3} – frac{1359425}{8} = 0$$
$$- frac{8000 x_{1}}{3} – frac{5000 x_{10}}{3} + frac{500 x_{11}}{3} – 1500 x_{12} – 500 x_{13} – frac{1750 x_{14}}{3} + frac{250 x_{15}}{3} + frac{4250 x_{16}}{3} – frac{1000 x_{17}}{3} + frac{2450 x_{5}}{3} + frac{5000 x_{6}}{3} + frac{2000 x_{7}}{3} + frac{1225 x_{8}}{3} – frac{1600 x_{9}}{3} + frac{168625}{2} = 0$$
Получаем ответ:
$$x_{1} = – x_{10} – frac{x_{11}}{2} – frac{x_{14}}{2} + frac{x_{15}}{2} + x_{16} + x_{17} – frac{3 x_{4}}{10} + frac{2 x_{5}}{5} + x_{6} + frac{2 x_{7}}{5} – frac{11 x_{8}}{20} – frac{x_{9}}{5} + frac{459}{40}$$
$$x_{1} = frac{11 x_{10}}{124} – frac{29 x_{11}}{124} – frac{39 x_{12}}{124} – frac{21 x_{13}}{124} + frac{53 x_{14}}{248} – frac{59 x_{15}}{248} + frac{65 x_{16}}{248} – frac{47 x_{17}}{124} – frac{6 x_{2}}{31} + frac{97 x_{5}}{1240} + frac{103 x_{6}}{124} + frac{10 x_{7}}{31} + frac{547 x_{8}}{2480} – frac{119 x_{9}}{310} + frac{98313}{4960}$$
$$x_{1} = – frac{17 x_{10}}{104} – frac{25 x_{11}}{104} – frac{15 x_{12}}{104} – frac{9 x_{13}}{104} + frac{25 x_{14}}{208} + frac{17 x_{15}}{208} + frac{205 x_{16}}{208} + frac{29 x_{17}}{104} + frac{3 x_{3}}{13} + frac{73 x_{5}}{208} + frac{179 x_{6}}{104} + frac{17 x_{7}}{26} + frac{43 x_{8}}{416} – frac{11 x_{9}}{52} – frac{163131}{4160}$$
$$x_{1} = – frac{5 x_{10}}{8} + frac{x_{11}}{16} – frac{9 x_{12}}{16} – frac{3 x_{13}}{16} – frac{7 x_{14}}{32} + frac{x_{15}}{32} + frac{17 x_{16}}{32} – frac{x_{17}}{8} + frac{49 x_{5}}{160} + frac{5 x_{6}}{8} + frac{x_{7}}{4} + frac{49 x_{8}}{320} – frac{x_{9}}{5} + frac{4047}{128}$$
где x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17 – свободные переменные
