Calculo

´
UNIVERSIDAD TECNOLOGICA DE PUEBLA.
CARRERA TECNOLOGIA AMBIENTAL
1E
Profra. Mirna P. Ju´rez Varela
a

Chapter 1

1.1
En los siguientes ejercicios encuentre las soluciones ( si existen) a los sistemas dados.
3x1 + 6x2 = 9
−2x1 + 3x2 = 4

(1.1)

3x1 + 6x2 = 9
2x1 + 4x2 = 6

(1.2)

3x1 − 6x2 = 9
2x1 + 4x2 = 6

(1.3)

2x1 + 3x2 = −1
−7x1 + 4x2 = 47

(1.4)

3x1 − x2 =0
4x1 + 2x2 = 5

(1.5)

2x1 + x2 + x3 = 6
3x1 − 2x2 − 3x3 = 5
8x1 + 2x2 + 5x3 = 11

x1 + x2 + x3 = 8
4x2 − x3 = −2
3x1 − x2 + 2x3 = 0
1

(1.6)

(1.7)

2x1 + 2x2 + x3 = 7
x1 + 2x2 + x3 = 0
−x1 + x2 + 3x3 = 1

2x1 + 5x2 − x3 = −1
4x1 + x2 + 3x3 = 3

(1.8)

(1.9)

−2x1 + 2x2 = 0

2x1 + x2 − x3 = 4
x1 + 3x3 = 2
−x2 + 5x3 = 1

(1.10)

x1 + x2 + x3 = 2
2x1 − x2 +2x3 = 4
−3x1 + 2x2 + 3x3 = 8

(1.11)

x1 + x2 + x3 = 0
2x1 − x2 + 2x3 = 0
−3x1 + 2x2 + 3x3 = 0

(1.12)

x1 + x2 + x3 = 2
2x1 − x2 + 2x3 = 4
−x1 + 4x2 + x3 = 2

(1.13)

x1 + x2 + x3 = 2
2x1 − x2 + 2x3 = 4
−x1 + 4x2 + 3x3 = 3

(1.14)

x1 + x2 + x3 = 0
2x1 − x2 + 2x3 = 0
−x1 + 4x2 + x3 = 0
2

(1.15)

En los ejercicios siguientes realice los clculos indicados



2
13
−2 1
4
5  −1 2 4  − 3  5
0
7
−6 1 5
2
−1 3
10
2 −1
23
06

3
6

+

15
24

2
3
−1 4


2
35
 −1 6 4  
1
06

2
04
−2 5 8


571
2 0 3


1 0 0
056
5 −1
27


0
−1 2
3
1
2
−7 3
5


7
1
2
3

1 0 3 −1 5 
 −1 0 


2162
5
5
6
2
3



1 −1 2
2
3 5
6  1 
24
−1
3

(1.16)

(1.17)(1.18)

(1.19)

(1.20)

(1.21)

(1.22)

En los siguientes problemas eval´ e el determinante
u
−1
3
2

02
14
0 −6

21
3 −2
51
−3
1
−1

−1
0
6

(1.24)

2
4
−1 2
4
0

(1.25)

0 −2
12
40
−2
4
−2

(1.23)

3
−3
5

36
18
00
3

(1.26)

(1.27)

2 −1
40
5 −2

3
6
3

(1.28)

´
Alvarez Aquino (1.1), (1.3), (1.5), (1.9), (1.11), (1.13),(1.16), (1.20), (1.25), (1.28)
Arias Valdivia (1.2), (1.4), (1.8), (1.11), (1.13), (1.16), (1.18), (1.21), (1.24), (1.27)
´
Avila Cedillo (1.3), (1.5), (1.9), (1.12), (1.14), (1.16), (1.19), (1.22), (1.25), (1.28)
Conde Cruz (1.4), (1.7), (1.8), (1.11), (1.13), (1.16), (1.19) (1.23), (1.25), (1.27)
Cruz Jim´nez (1.1), (1.3), (1.7), (1.10), (1.12), (1.15), (1.17), (1.20), (1.23), (1.26)
eD´vila Ru´ (1.1), (1.5), (1.12), (1.16), (1.17), (1.24), (1.25), (1.20), (1.8), (1.3)
a
ız
Flores Cote (1.3), (1.7), (1.10), (1.16), (1.20), (1.23), (1.26), (1.1), (1.12), (1.15)
Garc´ Almaraz (1.2), (1.8), (1.13), (1.14), (1.18), (1.22), (1.27) (1.3), (1.7), (1.22)
ıa
Jaimes Benitez (1.4), (1.9), (1.11), (??, (1.19), (1.21), (1.28), (1.22), (1.1), (1.14)
Landa Montero A (1.1), (1.4), (1.8),(1.11), (1.12), (1.15), (1.18) (1.21), (1.24), (1.27)
Landa Montero S (1.2), (1.5), (1.9), (1.10), (1.13), (1.16), (1.19), (1.22), (1.25), (1.28)
Le´n Ram´
o
ırez (1.3), (1.7), (1.8), (1.12), (1.13), (1.16), (1.20), (1.23), (1.24), (1.27)
Loaiza Ortiz (1.1), (1.4), (1.9), (1.10), (1.15), (1.17), (1.19), (1.22), (1.25), (1.28)
L´pez Cort´s (1.2), (1.5), (1.9), (1.11), (1.14), (1.16), (1.18),(1.21), (1.26), (1.27)
o
e
L´pez Hern´ndez (1.1), (1.4), (1.8), (1.11), (1.15), (1.16), (1.19), (1.22), (1.25), (1.27)
o
a
L´pez Salas (1.2), (1.5), (1.10), (1.12), (1.14), (1.17), (1.20), (1.23), (1.26), (1.28)
o
Mart´
ınez Hern´ndez Ram´n (1.3), (1.5), (1.9), (1.13), (1.16), (1.18), (1.21), (1.24), (1.26),
a
o
(1.27)
Mart´
ınez Hern´ndez Raymundo (1.2), (1.4), (1.8), (1.13), (1.16),(1.17), (1.21), (1.22), (1.26),
a
(1.28)
Morales Flores (1.1), (??, (1.9), (1.12), (1.15), (1.18), (1.20), (1.23), (1.25), (1.28)
Nahuatlato Ju´rez (1.3), (1.7), (1.10), (1.11), (1.14), (1.16), (1.19), (1.24), (1.25), (1.27)
a
Osorio Arroyo (1.1), (1.4), (1.10), (1.11), (1.16), (1.16), (1.21), (1.24), (1.26), (1.27)
Paredes Castillo (1.3), (1.5), (1.9), (1.13), (1.14), (1.17), (1.20),...