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DESCARGA
CAPITULO XXV

Hallar el valor de una determinante de tercer orden
Ejercicio 187
Hallar el valor de las siguientes determinantes:
  1. | 1 2 1 1 3 4 1 0 2 | | 1 2 1 1 3 4 1 0 2 1 2 1 1 3 4 | = [(1 × 3 × 2 ) +(1 × 0 × 1 ) +(1 × 2 × 4 ) ] –[(1 × 3 × 1 ) +(4 × 0 × 1 ) +(2 × 2 × 1 ) ] = [6+0+8 ] –[3+0+4 ] = 14–7 = 7
  2. | 1 2 – 2 1 – 3 3 – 1 4 5 | | 1 2 – 2 1 – 3 3 – 1 4 5 1 2 – 2 1 – 3 3 | = [(1 × –3 × 5 ) +(1 × 4 × –2 ) +(–1 × 2 × 3 ) ] –[(–2 × –3 × –1 ) +(3 × 4 × 1 ) +(5 × 2 × 1 ) ] = [–15–8–6 ] –[–6+12+10 ] = –29–16 = –45
  3. | – 3 4 1 2 – 3 0 1 2 7 | | – 3 4 1 2 – 3 0 1 2 7 – 3 4 1 2 – 3 0 | = [(–3 × –3 × 7 ) +(2 × 2 × 1 ) +(1 × 4 × 0 ) ] –[(1 × –3 × –1 ) +(–3 × 2 × 0 ) +(2 × 4 × 7 ) ] = [63+4+0 ] –[–3+0+56 ] = 67–53 = 14
  4. | 2 5 – 1 3 – 4 3 6 2 4 | | 2 5 – 1 3 – 4 3 6 2 4 2 5 – 1 3 – 4 3 | = [(2 × –4 × 4 ) +(3 × 2 × –1 ) +(6 × 5 × 3 ) ] –[(–1 × –4 × 6 ) +(2 × 2 × 3 ) +(3 × 5 × 4 ) ] = [–32–6+90 ] –[24+12+60 ] = 52–96 = –44
  5. | 5 – 1 – 6 – 2 5 3 3 4 2 | | 5 – 1 – 6 – 2 5 3 3 4 2 5 – 1 – 6 – 2 5 3 | = [(5 × 5 × 2 ) +(–2 × 4 × –6 ) +(3 × –1 × 3 ) ] –[(3 × 5 × –6 ) +(5 × 4 × 3 ) +(–2 × –1 × 2 ) ] = [50+48–9 ] –[–90+60+4 ] = 89+26 = 115
  6. | 4 1 5 3 2 – 6 12 3 2 | | 4 1 5 3 2 – 6 12 3 2 4 1 5 3 2 – 6 | = [(4 × 2 × 2 ) +(3 × 3 × 5 ) +(12 × 1 × –6 ) ] –[(12 × 2 × 5 ) +(4 × 3 × –6 ) +(3 × 1 × 2 ) ] = [16+45–72 ] –[120–72+6 ] = –11–54 = –65
  7. | 5 2 – 8 – 3 – 7 3 4 0 – 1 | | 5 2 – 8 – 3 – 7 3 4 0 – 1 5 2 – 8 – 3 – 7 3 | = [(5 × –7 × –1 ) +(–3 × 0 × –8 ) +(4 × 2 × 3 ) ] –[(4 × –7 × –8 ) +(5 × 0 × 3 ) +(–3 × 2 × –1 ) ] = [35+0+24 ] –[224+0+6 ] = 59–230 = –171
  8. | 3 2 5 – 1 – 3 4 3 2 5 | | 3 2 5 – 1 – 3 4 3 2 5 3 2 5 – 1 – 3 4 | = [(3 × –3 × 5 ) +(–1 × 2 × 5 ) +(3 × 2 × 4 ) ] –[(3 × –3 × 5 ) +(3 × 2 × 4 ) +(–1 × 2 × 5 ) ] = [–45–10+24 ] –[–45+24–10 ] = –31+31 = 0
  9. | 5 2 3 6 1 2 3 4 5 | | 5 2 3 6 1 2 3 4 5 5 2 3 6 1 2 | = [(5 × 1 × 5 ) +(6 × 4 × 3 ) +(3 × 2 × 2 ) ] –[(3 × 1 × 3 ) +(5 × 4 × 2 ) +(6 × 2 × 5 ) ] = [25+72+12 ] –[9+40+60 ] = 109–109 = 0
  10. | 12 5 10 8 – 6 9 7 4 – 2 | | 12 5 10 8 – 6 9 7 4 – 2 12 5 10 8 – 6 9 | = [(12 × –6 × –2 ) +(8 × 4 × 10 ) +(7 × 5 × 9 ) ] –[(7 × –6 × 10 ) +(12 × 4 × 9 ) +(8 × 5 × –2 ) ] = [144+320+315 ] –[–420+432–80 ] = 779+68 = 847
  11. | – 9 3 – 4 7 – 5 – 3 4 6 1 | | – 9 3 – 4 7 – 5 – 3 4 6 1 – 9 3 – 4 7 – 5 – 3 | = [(–9 × –5 × 1 ) +(7 × 6 × –4 ) +(4 × 3 × –3 ) ] –[(4 × –5 × –4 ) +(–9 × 6 × –3 ) +(7 × 3 × 1 ) ] = [45–168–36 ] –[80+162+21 ] = –159–263 = –422
  12. | 11 – 5 7 – 12 3 8 – 13 1 9 | | 11 – 5 7 – 12 3 8 – 13 1 9 11 – 5 7 – 12 3 8 | = [(11 × 3 × 9 ) +(–12 × 1 × 7 ) +(–13 × –5 × 8 ) ] –[(–13 × 3 × 7 ) +(11 × 1 × 8 ) +(–12 × –5 × 9 ) ] = [297–84+520 ] –[–273+88+540 ] = 733–355 = 378
Categories: Capítulo XXV