Ejercicio 188

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CAPITULO XXV

Ecuaciones simultáneas con tres incógnitas
Resolución por determinantes
Ejercicio 188
Resolver por determinantes:
  1. { x+y+z=11 xy+3z=13 2x+2yz=7 x = | 11 1 1 13 1 3 7 2 1 | | 1 1 1 1 1 3 2 2 1 | = | 11 1 1 13 1 3 7 2 1 11 1 1 13 1 3 | | 1 1 1 1 1 3 2 2 1 1 1 1 1 1 3 | = [(11 × 1 × 1 ) +(13 × 2 × 1 ) +(7 × 1 × 3 ) ] [(7 × 1 × 1 ) +(11 × 2 × 3 ) +(1 × 1 × 13 ) ] [(1 × 1 × 1 ) +(1 × 2 × 1 ) +(2 × 1 × 3 ) ] [(2 × 1 × 1 ) +(1 × 2 × 3 ) +(1 × 1 × 1 ) ] = [11+26+21 ] [7+6613 ] [1+2+6 ] [2+61 ] = 5846 93 = 6 = 2 y = | 1 11 1 1 13 3 2 7 1 | | 1 1 1 1 1 3 2 2 1 | = | 1 11 1 1 13 3 2 7 1 1 11 1 1 13 3 | | 1 1 1 1 1 3 2 2 1 1 1 1 1 1 3 | = [(1 × 13 × 1 ) +(1 × 7 × 1 ) +(2 × 11 × 3 ) ] [(2 × 13 × 1 ) +(1 × 7 × 3 ) +(1 × 11 × 1 ) ] [(1 × 1 × 1 ) +(1 × 2 × 1 ) +(2 × 1 × 3 ) ] [(2 × 1 × 1 ) +(1 × 2 × 3 ) +(1 × 1 × 1 ) ] = [13+7+66 ] [26+2111 ] [1+2+6 ] [2+61 ] = 6036 93 = 6 = 4 z = | 1 1 11 1 1 13 2 2 7 | | 1 1 1 1 1 3 2 2 1 | = | 1 1 11 1 1 13 2 2 7 1 1 11 1 1 13 | | 1 1 1 1 1 3 2 2 1 1 1 1 1 1 3 | = [(1 × 1 × 7 ) +(1 × 2 × 11 ) +(2 × 1 × 13 ) ] [(2 × 1 × 11 ) +(1 × 2 × 13 ) +(1 × 1 × 7 ) ] [(1 × 1 × 1 ) +(1 × 2 × 1 ) +(2 × 1 × 3 ) ] [(2 × 1 × 1 ) +(1 × 2 × 3 ) +(1 × 1 × 1 ) ] = [7+22+26 ] [22+26+7 ] [1+2+6 ] [2+61 ] = 4111 93 = 6 = 5 Sol.{ x=2 y=4 z=5
  2. { x+y+z=6 2x+yz=1 x2y+3z=6 x = | 6 1 1 1 1 1 6 2 3 | | 1 1 1 2 1 1 1 2 3 | = | 6 1 1 1 1 1 6 2 3 6 1 1 1 1 1 | | 1 1 1 2 1 1 1 2 3 1 1 1 2 1 1 | = [(6 × 1 × 3 ) +(1 × 2 × 1 ) +(6 × 1 × 1 ) ] [(6 × 1 × 1 ) +(6 × 2 × 1 ) +(1 × 1 × 3 ) ] [(1 × 1 × 3 ) +(2 × 2 × 1 ) +(1 × 1 × 1 ) ] [(1 × 1 × 1 ) +(1 × 2 × 1 ) +(2 × 1 × 3 ) ] = [18+2+6 ] [6123 ] [341 ] [1+2+6 ] = 10+21 29 = 11 11 = 1 y = | 1 6 1 2 1 1 1 6 3 | | 1 1 1 2 1 1 1 2 3 | = | 1 6 1 2 1 1 1 6 3 1 6 1 2 1 1 | | 1 1 1 2 1 1 1 2 3 1 1 1 2 1 1 | = [(1 × 1 × 3 ) +(2 × 6 × 1 ) +(1 × 6 × 1 ) ] [(1 × 1 × 1 ) +(1 × 6 × 1 ) +(2 × 6 × 3 ) ] [(1 × 1 × 3 ) +(2 × 2 × 1 ) +(1 × 1 × 1 ) ] [(1 × 1 × 1 ) +(1 × 2 × 1 ) +(2 × 1 × 3 ) ] = [312+6 ] [1+636 ] [341 ] [1+2+6 ] = 9+31 29 = 11 = 2 z = | 1 1 6 2 1 1 1 2 6 | | 1 1 1 2 1 1 1 2 3 | = | 1 1 6 2 1 1 1 2 6 1 1 6 2 1 1 | | 1 1 1 2 1 1 1 2 3 1 1 1 2 1 1 | = [(1 × 1 × 6 ) +(2 × 2 × 6 ) +(1 × 1 × 1 ) ] [(1 × 1 × 6 ) +(1 × 2 × 1 ) +(2 × 1 × 6 ) ] [(1 × 1 × 3 ) +(2 × 2 × 1 ) +(1 × 1 × 1 ) ] [(1 × 1 × 1 ) +(1 × 2 × 1 ) +(2 × 1 × 3 ) ] = [6+241 ] [6+212 ] [341 ] [1+2+6 ] = 17+16 29 = 11 = 3 Sol.{ x=1 y=2 z=3
  3. { 2x+3y+4z=3 2x+6y+8z=5 4x+9y4z=4 x = | 3 3 4 5 6 8 4 9 4 | | 2 3 4 2 6 8 4 9 4 | = | 3 3 4 5 6 8 4 9 4 3 3 4 5 6 8 | | 2 3 4 2 6 8 4 9 4 2 3 4 2 6 8 | = [(3 × 6 × 4 ) +(5 × 9 × 4 ) +(4 × 3 × 8 ) ] [(4 × 6 × 4 ) +(3 × 9 × 8 ) +(5 × 3 × 4 ) ] [(2 × 6 × 4 ) +(2 × 9 × 4 ) +(4 × 3 × 8 ) ] [(4 × 6 × 4 ) +(2 × 9 × 8 ) +(2 × 3 × 4 ) ] = [72+180+96 ] [96+21660 ] [48+72+96 ] [96+14424 ] = 204252 120216 = 48 = 1 2 y = | 2 3 4 2 5 8 4 4 4 | | 2 3 4 2 6 8 4 9 4 | = | 2 3 4 2 5 8 4 4 4 2 3 4 2 5 8 | | 2 3 4 2 6 8 4 9 4 2 3 4 2 6 8 | = [(2 × 5 × 4 ) +(2 × 4 × 4 ) +(4 × 3 × 8 ) ] [(4 × 5 × 4 ) +(2 × 4 × 8 ) +(2 × 3 × 4 ) ] [(2 × 6 × 4 ) +(2 × 9 × 4 ) +(4 × 3 × 8 ) ] [(4 × 6 × 4 ) +(2 × 9 × 8 ) +(2 × 3 × 4 ) ] = [40+32+96 ] [80+6424 ] [48+72+96 ] [96+14424 ] = 88120 120216 = 32 = 1 3 z = | 2 3 3 2 6 5 4 9 4 | | 2 3 4 2 6 8 4 9 4 | = | 2 3 3 2 6 5 4 9 4 2 3 3 2 6 5 | | 2 3 4 2 6 8 4 9 4 2 3 4 2 6 8 | = [(2 × 6 × 4 ) +(2 × 9 × 3 ) +(4 × 3 × 5 ) ] [(4 × 6 × 3 ) +(2 × 9 × 5 ) +(2 × 3 × 4 ) ] [(2 × 6 × 4 ) +(2 × 9 × 4 ) +(4 × 3 × 8 ) ] [(4 × 6 × 4 ) +(2 × 9 × 8 ) +(2 × 3 × 4 ) ] = [48+54+60 ] [72+90+24 ] [48+72+96 ] [96+14424 ] = 162186 120216 = 24 = 1 4 Sol.{ x= 1 2 y= 1 3 z= 1 4
  4. { 4xy+z=4 2yz+2x=2 6x+3z2y=12 { 4xy+z=4 2x+2yz=2 6x2y+3z=12 x = | 4 1 1 2 2 1 12 2 3 | | 4 1 1 2 2 1 6 2 3 | = | 4 1 1 2 2 1 12 2 3 4 1 1 2 2 1 | | 4 1 1 2 2 1 6 2 3 4 1 1 2 2 1 | = [(4 × 2 × 3 ) +(2 × 2 × 1 ) +(12 × 1 × 1 ) ] [(12 × 2 × 1 ) +(4 × 2 × 1 ) +(2 × 1 × 3 ) ] [(4 × 2 × 3 ) +(2 × 2 × 1 ) +(6 × 1 × 1 ) ] [(6 × 2 × 1 ) +(4 × 2 × 1 ) +(2 × 1 × 3 ) ] = [244+12 ] [24+86 ] [244+6 ] [12+86 ] = 3226 2614 = 6 = 1 2 y = | 4 4 1 2 2 1 6 12 3 | | 4 1 1 2 2 1 6 2 3 | = | 4 4 1 2 2 1 6 12 3 4 4 1 2 2 1 | | 4 1 1 2 2 1 6 2 3 4 1 1 2 2 1 | = [(4 × 2 × 3 ) +(2 × 12 × 1 ) +(6 × 4 × 1 ) ] [(6 × 2 × 1 ) +(4 × 12 × 1 ) +(2 × 4 × 3 ) ] [(4 × 2 × 3 ) +(2 × 2 × 1 ) +(6 × 1 × 1 ) ] [(6 × 2 × 1 ) +(4 × 2 × 1 ) +(2 × 1 × 3 ) ] = [24+2424 ] [1248+24 ] [244+6 ] [12+86 ] = 24+12 2614 = 12 = 3 z = | 4 1 4 2 2 2 6 2 12 | | 4 1 1 2 2 1 6 2 3 | = | 4 1 4 2 2 2 6 2 12 4 1 4 2 2 2 | | 4 1 1 2 2 1 6 2 3 4 1 1 2 2 1 | = [(4 × 2 × 12 ) +(2 × 2 × 4 ) +(6 × 1 × 2 ) ] [(6 × 2 × 4 ) +(4 × 2 × 2 ) +(2 × 1 × 12 ) ] [(4 × 2 × 3 ) +(2 × 2 × 1 ) +(6 × 1 × 1 ) ] [(6 × 2 × 1 ) +(4 × 2 × 1 ) +(2 × 1 × 3 ) ] = [961612 ] [481624 ] [244+6 ] [12+86 ] = 688 2614 = 12 = 5 Sol.{ x= 1 2 y=3 z=5
  5. { x+4y+5z=11 3x2y+z=5 4x+y3z=26 x = | 11 4 5 5 2 1 26 1 3 | | 1 4 5 3 2 1 4 1 3 | = | 11 4 5 5 2 1 26 1 3 11 4 5 5 2 1 | | 1 4 5 3 2 1 4 1 3 1 4 5 3 2 1 | = [(11 × 2 × 3 ) +(5 × 1 × 5 ) +(26 × 4 × 1 ) ] [(26 × 2 × 5 ) +(11 × 1 × 1 ) +(5 × 4 × 3 ) ] [(1 × 2 × 3 ) +(3 × 1 × 5 ) +(4 × 4 × 1 ) ] [(4 × 2 × 5 ) +(1 × 1 × 1 ) +(3 × 4 × 3 ) ] = [66+25104 ] [260+1160 ] [6+15+16 ] [40+136 ] = 13211 37+75 = 112 = 2 y = | 1 11 5 3 5 1 4 26 3 | | 1 4 5 3 2 1 4 1 3 | = | 1 11 5 3 5 1 4 26 3 1 11 5 3 5 1 | | 1 4 5 3 2 1 4 1 3 1 4 5 3 2 1 | = [(1 × 5 × 3 ) +(3 × 26 × 5 ) +(4 × 11 × 1 ) ] [(4 × 5 × 5 ) +(1 × 26 × 1 ) +(3 × 11 × 3 ) ] [(1 × 2 × 3 ) +(3 × 1 × 5 ) +(4 × 4 × 1 ) ] [(4 × 2 × 5 ) +(1 × 1 × 1 ) +(3 × 4 × 3 ) ] = [15390+44 ] [1002699 ] [6+15+16 ] [40+136 ] = 361+25 37+75 = 112 = 3 z = | 1 4 11 3 2 5 4 1 26 | | 1 4 5 3 2 1 4 1 3 | = | 1 4 11 3 2 5 4 1 26 1 4 11 3 2 5 | | 1 4 5 3 2 1 4 1 3 1 4 5 3 2 1 | = [(1 × 2 × 26 ) +(3 × 1 × 11 ) +(4 × 4 × 5 ) ] [(4 × 2 × 11 ) +(1 × 1 × 5 ) +(3 × 4 × 26 ) ] [(1 × 2 × 3 ) +(3 × 1 × 5 ) +(4 × 4 × 1 ) ] [(4 × 2 × 5 ) +(1 × 1 × 1 ) +(3 × 4 × 3 ) ] = [52+33+80 ] [88+5312 ] [6+15+16 ] [40+136 ] = 165+395 37+75 = 112 = 5 Sol.{ x=2 y=3 z=5
  6. { 7x+10y+4z=2 5x2y+6z=38 3x+yz=21 x = | 2 10 4 38 2 6 21 1 1 | | 7 10 4 5 2 6 3 1 1 | = | 2 10 4 38 2 6 21 1 1 2 10 4 38 2 6 | | 7 10 4 5 2 6 3 1 1 7 10 4 5 2 6 | = [(2 × 2 × 1 ) +(38 × 1 × 4 ) +(21 × 10 × 6 ) ] [(21 × 2 × 4 ) +(2 × 1 × 6 ) +(38 × 10 × 1 ) ] [(7 × 2 × 1 ) +(5 × 1 × 4 ) +(3 × 10 × 6 ) ] [(3 × 2 × 4 ) +(7 × 1 × 6 ) +(5 × 10 × 1 ) ] = [4+152+1260 ] [16812380 ] [14+20+180 ] [24+4250 ] = 1408+560 214+32 = 246 = 8 y = | 7 2 4 5 38 6 3 21 1 | | 7 10 4 5 2 6 3 1 1 | = | 7 2 4 5 38 6 3 21 1 7 2 4 5 38 6 | | 7 10 4 5 2 6 3 1 1 7 10 4 5 2 6 | = [(7 × 38 × 1 ) +(5 × 21 × 4 ) +(3 × 2 × 6 ) ] [(3 × 38 × 4 ) +(7 × 21 × 6 ) +(5 × 2 × 1 ) ] [(7 × 2 × 1 ) +(5 × 1 × 4 ) +(3 × 10 × 6 ) ] [(3 × 2 × 4 ) +(7 × 1 × 6 ) +(5 × 10 × 1 ) ] = [266+42036 ] [456+882+10 ] [14+20+180 ] [24+4250 ] = 1181348 214+32 = 246 = 5 z = | 7 10 2 5 2 38 3 1 21 | | 7 10 4 5 2 6 3 1 1 | = | 7 10 2 5 2 38 3 1 21 7 10 2 5 2 38 | | 7 10 4 5 2 6 3 1 1 7 10 4 5 2 6 | = [(7 × 2 × 21 ) +(5 × 1 × 2 ) +(3 × 10 × 38 ) ] [(3 × 2 × 2 ) +(7 × 1 × 38 ) +(5 × 10 × 21 ) ] [(7 × 2 × 1 ) +(5 × 1 × 4 ) +(3 × 10 × 6 ) ] [(3 × 2 × 4 ) +(7 × 1 × 6 ) +(5 × 10 × 1 ) ] = [29410+1140 ] [12+266+1050 ] [14+20+180 ] [24+4250 ] = 8361328 214+32 = 246 = 2 Sol.{ x=8 y=5 z=2
  7. { 4x+7y+5z=2 6x+3y+7z=6 xy+9z=21 x = | 2 7 5 6 3 7 21 1 9 | | 4 7 5 6 3 7 1 1 9 | = | 2 7 5 6 3 7 21 1 9 2 7 5 6 3 7 | | 4 7 5 6 3 7 1 1 9 4 7 5 6 3 7 | = [(2 × 3 × 9 ) +(6 × 1 × 5 ) +(21 × 7 × 7 ) ] [(21 × 3 × 5 ) +(2 × 1 × 7 ) +(6 × 7 × 9 ) ] [(4 × 3 × 9 ) +(6 × 1 × 5 ) +(1 × 7 × 7 ) ] [(1 × 3 × 5 ) +(4 × 1 × 7 ) +(6 × 7 × 9 ) ] = [54301029 ] [315+14+378 ] [10830+49 ] [1528+378 ] = 111377 127365 = 238 = 5 y = | 4 2 5 6 6 7 1 21 9 | | 4 7 5 6 3 7 1 1 9 | = | 4 2 5 6 6 7 1 21 9 4 2 5 6 6 7 | | 4 7 5 6 3 7 1 1 9 4 7 5 6 3 7 | = [(4 × 6 × 9 ) +(6 × 21 × 5 ) +(1 × 2 × 7 ) ] [(1 × 6 × 5 ) +(4 × 21 × 7 ) +(6 × 2 × 9 ) ] [(4 × 3 × 9 ) +(6 × 1 × 5 ) +(1 × 7 × 7 ) ] [(1 × 3 × 5 ) +(4 × 1 × 7 ) +(6 × 7 × 9 ) ] = [21663014 ] [30588108 ] [10830+49 ] [1528+378 ] = 452+666 127365 = 238 238 = 1 z = | 4 7 2 6 3 6 1 1 21 | | 4 7 5 6 3 7 1 1 9 | = | 4 7 2 6 3 6 1 1 21 4 7 2 6 3 6 | | 4 7 5 6 3 7 1 1 9 4 7 5 6 3 7 | = [(4 × 3 × 21 ) +(6 × 1 × 2 ) +(1 × 7 × 6 ) ] [(1 × 3 × 2 ) +(4 × 1 × 6 ) +(6 × 7 × 21 ) ] [(4 × 3 × 9 ) +(6 × 1 × 5 ) +(1 × 7 × 7 ) ] [(1 × 3 × 5 ) +(4 × 1 × 7 ) +(6 × 7 × 9 ) ] = [252+12+42 ] [624882 ] [10830+49 ] [1528+378 ] = 198+912 127365 = 238 = 3 Sol.{ x=5 y=1 z=3
  8. { 3x5y+2z=22 2xy+6z=32 8x+3y5z=33 x = | 22 5 2 32 1 6 33 3 5 | | 3 5 2 2 1 6 8 3 5 | = | 22 5 2 32 1 6 33 3 5 22 5 2 32 1 6 | | 3 5 2 2 1 6 8 3 5 3 5 2 2 1 6 | = [(22 × 1 × 5 ) +(33 × 3 × 2 ) +(33 × 5 × 6 ) ] [(33 × 1 × 2 ) +(22 × 3 × 6 ) +(32 × 5 × 5 ) ] [(3 × 1 × 5 ) +(2 × 3 × 2 ) +(8 × 5 × 6 ) ] [(8 × 1 × 2 ) +(3 × 3 × 6 ) +(2 × 5 × 5 ) ] = [110+192+990 ] [66396+800 ] [15+12240 ] [16+54+50 ] = 1072470 21388 = 301 = 2 y = | 3 22 2 2 32 6 8 33 5 | | 3 5 2 2 1 6 8 3 5 | = | 3 22 2 2 32 6 8 33 5 3 22 2 2 32 6 | | 3 5 2 2 1 6 8 3 5 3 5 2 2 1 6 | = [(3 × 32 × 5 ) +(2 × 33 × 2 ) +(8 × 22 × 6 ) ] [(8 × 32 × 2 ) +(3 × 33 × 6 ) +(2 × 22 × 5 ) ] [(3 × 1 × 5 ) +(2 × 3 × 2 ) +(8 × 5 × 6 ) ] [(8 × 1 × 2 ) +(3 × 3 × 6 ) +(2 × 5 × 5 ) ] = [4801321056 ] [512594+220 ] [15+12240 ] [16+54+50 ] = 1668138 21388 = 301 = 6 z = | 3 5 22 2 1 32 8 3 33 | | 3 5 2 2 1 6 8 3 5 | = | 3 5 22 2 1 32 8 3 33 3 5 22 2 1 32 | | 3 5 2 2 1 6 8 3 5 3 5 2 2 1 6 | = [(3 × 1 × 33 ) +(2 × 3 × 22 ) +(8 × 5 × 32 ) ] [(8 × 1 × 22 ) +(3 × 3 × 32 ) +(2 × 5 × 33 ) ] [(3 × 1 × 5 ) +(2 × 3 × 2 ) +(8 × 5 × 6 ) ] [(8 × 1 × 2 ) +(3 × 3 × 6 ) +(2 × 5 × 5 ) ] = [991321280 ] [176+288+330 ] [15+12240 ] [16+54+50 ] = 1313795 21388 = 301 = 7 Sol.{ x=2 y=6 z=7
  9. { x+y+z=3 x+2y=6 2x+3y=6 x = | 3 1 1 6 2 0 6 3 0 | | 1 1 1 1 2 0 2 3 0 | = | 3 1 1 6 2 0 6 3 0 3 1 1 6 2 0 | | 1 1 1 1 2 0 2 3 0 1 1 1 1 2 0 | = [(3 × 2 × 0 ) +(6 × 3 × 1 ) +(6 × 1 × 0 ) ] [(6 × 2 × 1 ) +(3 × 3 × 0 ) +(6 × 1 × 0 ) ] [(1 × 2 × 0 ) +(1 × 3 × 1 ) +(2 × 1 × 0 ) ] [(2 × 2 × 1 ) +(1 × 3 × 0 ) +(1 × 1 × 0 ) ] = [0+18+0 ] [120+0 ] [0+30 ] [4+0+0 ] = 1812 34 = 6 1 = 6 y = | 1 3 1 1 6 0 2 6 0 | | 1 1 1 1 2 0 2 3 0 | = | 1 3 1 1 6 0 2 6 0 1 3 1 1 6 0 | | 1 1 1 1 2 0 2 3 0 1 1 1 1 2 0 | = [(1 × 6 × 0 ) +(1 × 6 × 1 ) +(2 × 3 × 0 ) ] [(2 × 6 × 1 ) +(1 × 6 × 0 ) +(1 × 3 × 0 ) ] [(1 × 2 × 0 ) +(1 × 3 × 1 ) +(2 × 1 × 0 ) ] [(2 × 2 × 1 ) +(1 × 3 × 0 ) +(1 × 1 × 0 ) ] = [0+6+0 ] [120+0 ] [0+30 ] [4+0+0 ] = 612 34 = 6 1 = 6 z = | 1 1 3 1 2 6 2 3 6 | | 1 1 1 1 2 0 2 3 0 | = | 1 1 3 1 2 6 2 3 6 1 1 3 1 2 6 | | 1 1 1 1 2 0 2 3 0 1 1 1 1 2 0 | = [(1 × 2 × 6 ) +(1 × 3 × 3 ) +(2 × 1 × 6 ) ] [(2 × 2 × 3 ) +(1 × 3 × 6 ) +(1 × 1 × 6 ) ] [(1 × 2 × 0 ) +(1 × 3 × 1 ) +(2 × 1 × 0 ) ] [(2 × 2 × 1 ) +(1 × 3 × 0 ) +(1 × 1 × 0 ) ] = [12+9+12 ] [12+18+6 ] [0+30 ] [4+0+0 ] = 3336 34 = 3 1 = 3 Sol.{ x=6 y=6 z=3
  10. { 3x2y=1 4x+z=28 x+2y+3z=43 x = | 1 2 0 28 0 1 43 2 3 | | 3 2 0 4 0 1 1 2 3 | = | 1 2 0 28 0 1 43 2 3 1 2 0 28 0 1 | | 3 2 0 4 0 1 1 2 3 3 2 0 4 0 1 | = [(1 × 0 × 3 ) +(28 × 2 × 0 ) +(43 × 2 × 1 ) ] [(43 × 0 × 0 ) +(1 × 2 × 1 ) +(28 × 2 × 3 ) ] [(3 × 0 × 3 ) +(4 × 2 × 0 ) +(1 × 2 × 1 ) ] [(1 × 0 × 0 ) +(3 × 2 × 1 ) +(4 × 2 × 3 ) ] = [0+0+86 ] [02+168 ] [0+02 ] [0+624 ] = 86166 2+18 = 16 = 5 y = | 3 1 0 4 28 1 1 43 3 | | 3 2 0 4 0 1 1 2 3 | = | 3 1 0 4 28 1 1 43 3 3 1 0 4 28 1 | | 3 2 0 4 0 1 1 2 3 3 2 0 4 0 1 | = [(3 × 28 × 3 ) +(4 × 43 × 0 ) +(1 × 1 × 1 ) ] [(1 × 28 × 0 ) +(3 × 43 × 1 ) +(4 × 1 × 3 ) ] [(3 × 0 × 3 ) +(4 × 2 × 0 ) +(1 × 2 × 1 ) ] [(1 × 0 × 0 ) +(3 × 2 × 1 ) +(4 × 2 × 3 ) ] = [252+01 ] [012912 ] [0+02 ] [0+624 ] = 253+141 2+18 = 16 = 7 z = | 3 2 1 4 0 28 1 2 43 | | 3 2 0 4 0 1 1 2 3 | = | 3 2 1 4 0 28 1 2 43 3 2 1 4 0 28 | | 3 2 0 4 0 1 1 2 3 3 2 0 4 0 1 | = [(3 × 0 × 43 ) +(4 × 2 × 1 ) +(1 × 2 × 28 ) ] [(1 × 0 × 1 ) +(3 × 2 × 28 ) +(4 × 2 × 43 ) ] [(3 × 0 × 3 ) +(4 × 2 × 0 ) +(1 × 2 × 1 ) ] [(1 × 0 × 0 ) +(3 × 2 × 1 ) +(4 × 2 × 3 ) ] = [08+56 ] [0168+344 ] [0+02 ] [0+624 ] = 48176 2+18 = 16 = 8 Sol.{ x=5 y=7 z=8
  11. { x 3 y 4 + z 4 =1 x 6 + y 2 z=1 x 2 y 8 z 2 =0 x = | 1 1 4 1 4 1 1 2 1 0 1 8 1 2 | | 1 3 1 4 1 4 1 6 1 2 1 1 2 1 8 1 2 | = | 1 1 4 1 4 1 1 2 1 0 1 8 1 2 1 1 4 1 4 1 1 2 1 | | 1 3 1 4 1 4 1 6 1 2 1 1 2 1 8 1 2 1 3 1 4 1 4 1 6 1 2 1 | = [(1 × 1 2 × 1 2 ) +(1 × 1 8 × 1 4 ) +(0 × 1 4 × 1 ) ] [(0 × 1 2 × 1 4 ) +(1 × 1 8 × 1 ) +(1 × 1 4 × 1 2 ) ] [( 1 3 × 1 2 × 1 2 ) +( 1 6 × 1 8 × 1 4 ) +( 1 2 × 1 4 × 1 ) ] [( 1 2 × 1 2 × 1 4 ) +( 1 3 × 1 8 × 1 ) +( 1 6 × 1 4 × 1 2 ) ] = [ 1 4 1 32 +0 ] [0+ 1 8 + 1 8 ] [ 1 12 1 192 + 1 8 ] [ 1 16 + 1 24 + 1 48 ] = 9 32 1 4 7 192 1 8 = 17 32 17 = 6 y = | 1 3 1 1 4 1 6 1 1 1 2 0 1 2 | | 1 3 1 4 1 4 1 6 1 2 1 1 2 1 8 1 2 | = | 1 3 1 1 4 1 6 1 1 1 2 0 1 2 1 3 1 1 4 1 6 1 1 | | 1 3 1 4 1 4 1 6 1 2 1 1 2 1 8 1 2 1 3 1 4 1 4 1 6 1 2 1 | = [( 1 3 × 1 × 1 2 ) +( 1 6 × 0 × 1 4 ) +( 1 2 × 1 × 1 ) ] [( 1 2 × 1 × 1 4 ) +( 1 3 × 0 × 1 ) +( 1 6 × 1 × 1 2 ) ] [( 1 3 × 1 2 × 1 2 ) +( 1 6 × 1 8 × 1 4 ) +( 1 2 × 1 4 × 1 ) ] [( 1 2 × 1 2 × 1 4 ) +( 1 3 × 1 8 × 1 ) +( 1 6 × 1 4 × 1 2 ) ] = [ 1 6 +0 1 2 ] [ 1 8 +0 1 12 ] [ 1 12 1 192 + 1 8 ] [ 1 16 + 1 24 + 1 48 ] = 2 3 1 24 7 192 1 8 = 17 24 17 = 8 z = | 1 3 1 4 1 1 6 1 2 1 1 2 1 8 0 | | 1 3 1 4 1 4 1 6 1 2 1 1 2 1 8 1 2 | = | 1 3 1 4 1 1 6 1 2 1 1 2 1 8 0 1 3 1 4 1 1 6 1 2 1 | | 1 3 1 4 1 4 1 6 1 2 1 1 2 1 8 1 2 1 3 1 4 1 4 1 6 1 2 1 | = [( 1 3 × 1 2 × 0 ) +( 1 6 × 1 8 × 1 ) +( 1 2 × 1 4 × 1 ) ] [( 1 2 × 1 2 × 1 ) +( 1 3 × 1 8 × 1 ) +( 1 6 × 1 4 × 0 ) ] [( 1 3 × 1 2 × 1 2 ) +( 1 6 × 1 8 × 1 4 ) +( 1 2 × 1 4 × 1 ) ] [( 1 2 × 1 2 × 1 4 ) +( 1 3 × 1 8 × 1 ) +( 1 6 × 1 4 × 1 2 ) ] = [0+ 1 48 1 8 ] [ 1 4 1 24 +0 ] [ 1 12 1 192 + 1 8 ] [ 1 16 + 1 24 + 1 48 ] = 7 48 5 24 7 192 1 8 = 17 48 17 = 4 Sol.{ x=6 y=8 z=4
  12. { x 3 +y=2z+3 xy=1 x+z= y 4 +11 { x 3 +y2z=3 xy=1 x y 4 +z=11 x = | 3 1 2 1 1 0 11 1 4 1 | | 1 3 1 2 1 1 0 1 1 4 1 | = | 3 1 2 1 1 0 11 1 4 1 3 1 2 1 1 0 | | 1 3 1 2 1 1 0 1 1 4 1 1 3 1 2 1 1 0 | = [(3 × 1 × 1 ) +(1 × 1 4 × 2 ) +(11 × 1 × 0 ) ] [(11 × 1 × 2 ) +(3 × 1 4 × 0 ) +(1 × 1 × 1 ) ] [( 1 3 × 1 × 1 ) +(1 × 1 4 × 2 ) +(1 × 1 × 0 ) ] [(1 × 1 × 2 ) +( 1 3 × 1 4 × 0 ) +(1 × 1 × 1 ) ] = [3+ 1 2 +0 ] [22+0+1 ] [ 1 3 + 1 2 +0 ] [2+0+1 ] = 5 2 23 1 6 3 = 2 17 = 9 y = | 1 3 3 2 1 1 0 1 11 1 | | 1 3 1 2 1 1 0 1 1 4 1 | = | 1 3 3 2 1 1 0 1 11 1 1 3 3 2 1 1 0 | | 1 3 1 2 1 1 0 1 1 4 1 1 3 1 2 1 1 0 | = [( 1 3 × 1 × 1 ) +(1 × 11 × 2 ) +(1 × 3 × 0 ) ] [(1 × 1 × 2 ) +( 1 3 × 11 × 0 ) +(1 × 3 × 1 ) ] [( 1 3 × 1 × 1 ) +(1 × 1 4 × 2 ) +(1 × 1 × 0 ) ] [(1 × 1 × 2 ) +( 1 3 × 1 4 × 0 ) +(1 × 1 × 1 ) ] = [ 1 3 22+0 ] [2+0+3 ] [ 1 3 + 1 2 +0 ] [2+0+1 ] = 65 3 1 1 6 3 = 3 17 = 8 z = | 1 3 1 3 1 1 1 1 1 4 11 | | 1 3 1 2 1 1 0 1 1 4 1 | = | 1 3 1 3 1 1 1 1 1 4 11 1 3 1 3 1 1 1 | | 1 3 1 2 1 1 0 1 1 4 1 1 3 1 2 1 1 0 | = [( 1 3 × 1 × 11 ) +(1 × 1 4 × 3 ) +(1 × 1 × 1 ) ] [(1 × 1 × 3 ) +( 1 3 × 1 4 × 1 ) +(1 × 1 × 11 ) ] [( 1 3 × 1 × 1 ) +(1 × 1 4 × 2 ) +(1 × 1 × 0 ) ] [(1 × 1 × 2 ) +( 1 3 × 1 4 × 0 ) +(1 × 1 × 1 ) ] = [ 11 3 3 4 +1 ] [3 1 12 +11 ] [ 1 3 + 1 2 +0 ] [2+0+1 ] = 41 12 95 12 1 6 3 = 17 6 = 4 Sol.{ x=9 y=8 z=4