Ejercicios Regla de Cramer. Sistema de ecuaciones

UNIVERSIDAD PRIVADA DE TACNA

FACULTAD DE INGENIERÍA

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TRABAJO ENCARGADO

“REGLA DE CRAMER”

ASIGNATURA        :        Matemática Básica

DOCENTE        :        Mag. Felipe Remigio Atencio Maquera

SECCIÓN        :        B

SEMESTRE :        2021 - II

INTEGRANTES        :        JIMÉNEZ CALDERÓN, ARIANA NICOLE (EPII)

MORENO ARIAS, GIAN MARCOS (EPIC) CHOQUECOTA TRONCOS, MARCOS (EPII) CABRERA CORNEJO, MICHAEL ANDREE (EPII)

TACNA – PERÚ 2021

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[pic 3]

{3𝑥 + 4𝑦 = −5 2𝑥 − 𝑦 = 4

𝐷 = [3        4 ] = (3)(-1)-(2)(4) = -11

2        −1

|𝐷𝑥| = [−5        4 ] = (−5)(−1) − (4)(4) = −11

4        −1

3        −5

( )( )        (

)( )

|𝐷𝑦| = [                ] =   3  2        4

4 − −5

2 = 22

|𝐷𝑋|        −11[pic 4][pic 5][pic 6]

𝑋 =

|𝐷| = −11 = 1

|𝐷𝑌|        22[pic 7][pic 8][pic 9]

𝑌 =

|𝐷| = −11 =

[pic 10]

{2𝑥 + 3𝑦 = 2

𝑥 − 2𝑦 = 8

𝐷 = [2        3 ] = (2) (-2)-(3)(1) = -7

1        −2

|𝐷 | = [2        3 ] = (2)(−2) − (8)(3) = −28[pic 11]

8        −2

2        2        ( )( )

( )( )

|𝐷𝑦| = [        ] =   2

8 − 1

2 = 14

1        8

𝑋 =

|𝐷𝑋|

|𝐷| =[pic 12]

−28

= 4[pic 13][pic 14]

−7

𝑌 = |𝐷𝑌| = 14 =-2[pic 15][pic 16][pic 17]

|𝐷|        −7

[pic 18]

𝑥 + 𝑦 − 𝑧 = 0

{2𝑥 − 3𝑦 + 𝑧 = 7

𝑥 + 2𝑦 − 𝑧 = 1

1        1        −1

𝐷 = [2        −3        1        ]

1        2        −1

D=(1)(−3)(−1)+(1)(1)(1)+(−1)(2)(2)−(1)(−3)(−1)−(2)(1)(1)−(−1)(2)(1)= −3

0        1        −1

|𝐷𝑥| = [7        −3        1        ]

1        2        −1

|Dx |=(0)(-3)(-1)+(1)(1)(1)+(-1)(7)(3)-(1)(-3)(-1)-(2)(1)(0)-(-1)(7)(1)= -9

1        0        −1

|𝐷𝑦| = [2        7        1        ]

1        1        −1

|Dy |=(1)(7)(−1)+(0)(1)(1)+(−1)(2)(1)−(1)(7)(−1)−(1)(1)(1)−(−1)(2)(0) = −3

...