Ejercicios para practicar de Optimizacion
Enviado por Andrea Molina • 13 de Junio de 2022 • Apuntes • 687 Palabras (3 Páginas) • 39 Visitas
Ejercicios para practicar:
- Dado el siguiente sistema de ecuaciones lineales:
[pic 1]
Respuestas: [pic 2]
- Dado el siguiente sistema de ecuaciones lineales:
[pic 3]
Respuestas: [pic 4]
Se pide para ambos casos:
- Resolver Usando determinante (Cubriendo filas y columnas) y después Cramer.
Necesitamos hallar el Dp
Ejercicio a)
[pic 5]
= + 3 * -2 +1[pic 6][pic 7][pic 8]
=3 (-3-4) -2(-5-4) +1(5-3)
3(-7) -2(-9) +1(2)
-21+18+2 = -1
[pic 9]
= + 1* -2 +1[pic 10][pic 11][pic 12]
= 1( -3-4) -2(-2-4) +1 (2-3)
= 1(-7) -2(-6) +1 ( -1)
=-7+ 12-1 = 4
[pic 13]
= + 3* -1 +1[pic 14][pic 15][pic 16]
= 3( -2-4) -1(-5-4) +1 (5-2)
= 3(-6) -1(-9) +1 (3)
= -18 + 9 + 3 = -6
[pic 17]
= + 3* -2 +1[pic 18][pic 19][pic 20]
= 3(3-2) -2(5-2) +1 (5-3)
= 3(1) -2(3) +1 (2)
= 3 -6 + 2 = -1
= = -4[pic 21][pic 22]
= = 6[pic 23][pic 24]
= = 1 [pic 25][pic 26]
Ejercicio b=
[pic 27]
= + 2 * -3 +5[pic 28][pic 29][pic 30]
=2 (0-12) -3(9-6) +5(6-0)
= 2 (-12) -3(3) +5(6)
= -24-9+30= -3
[pic 31]
= + 1 * -3 +5[pic 32][pic 33][pic 34]
=1 (0-12) -3(36-8) +5(24-0)
= 1 (-12) -3(28) +5(24)
X = -12-84+120= 24
[pic 35]
= + 2 * -1 +5[pic 36][pic 37][pic 38]
=2 (36-8) -1(9-6) +5(-4-12)
= 2 (28) -1(3) +5(-16)
Y = 56-3+80= 133
[pic 39]
= + 2 * -3 +1[pic 40][pic 41][pic 42]
=2 (0-24) -3(-4-12) +1(6-0)
= 2 (-24) -3(-16) +1(6)
Z = -48+48+6= 6
= = 8[pic 43][pic 44]
= [pic 45][pic 46]
= = -2[pic 47][pic 48]
- Resolver Usando determinante (Sarrus) y después Cramer
Ejercicio a)
[pic 49][pic 50]
[pic 51][pic 52][pic 53][pic 54][pic 55][pic 56]
[pic 57]
= (-9+ 5 +8) – (3+ 12- 10)
= (4 – 5)
= -1[pic 58]
[pic 59][pic 60][pic 61][pic 62][pic 63][pic 64]
[pic 65]
= (-3+ 2 +8) – (3+ 4- 4)
= (7 – 3)[pic 66][pic 67][pic 68][pic 69][pic 70][pic 71]
= 4[pic 72]
[pic 73]
= (-6+ 5 +4) – (2+ 12- 5)
= (3 – 9)[pic 74][pic 75][pic 76][pic 77][pic 78][pic 79]
= -6[pic 80]
[pic 81]
= (9+ 5 +4) – (3+ 6+ 10)
= (18 – 19)
= -1[pic 82]
Solución:
x= ; y= ; z= [pic 83][pic 84][pic 85]
x= = = -4[pic 86][pic 87]
y= = =[pic 88][pic 89][pic 90]
z= = = 1[pic 91][pic 92]
Ejercicio b)
[pic 93]
[pic 94][pic 95]
[pic 96][pic 97][pic 98][pic 99][pic 100][pic 101]
[pic 102]
= (0+ 30 +18) – (0+ 24+ 27)
= (48 – 51)[pic 103][pic 104][pic 105]
= -3[pic 107][pic 108][pic 109][pic 106]
[pic 110]
= (0+ 120 -24) – (0+ 12+ 108)
= (96 – 120)
= -24[pic 112][pic 113][pic 114][pic 115][pic 116][pic 117][pic 111]
...