Dario Mayo.docx

UNIVERSIDAD NACIONAL DE CHIMBORAZO Trabajo de Álgebra Escuela: Ing. Electrónica y Telecomunicaciones Por: Mayo Torres Darío José Ing. Clever Torres Fecha: 29/11/2017

Método de Cramer y Gauss Yordan.

2𝑥 1 − 5𝑥 2 + 𝑥 3 = 6 {−𝑥 1 + 4𝑥 2 − 𝑥 3 = −1} 2𝑥 1 + 5𝑥 2 = 3 Método de Cramer

2 −5 1 A= −1 4 −1 2 5 0

=[ 0 + 10 -5 ] – [ 8 + 0 – 10 ] = 5 + 2 = 7

6 −5 1 ΔX₁= −1 4 −1 3 5 0

= [ 0 + 15 – 5 ] – [ 12 - 30 + 0 ] = 10 + 18 = 28

2 6 1 ΔX₂= −1 −1 −1 2 3 0

2 −5 6 ΔX₃= −1 4 1 2 5 3

= [ 0 – 12 - 3 ] – [ - 2 - 6 – 0 ] = -15 + 8 = -7

= [ 24 – 30 + 10 ] – [ 48 + 15 – 10 ] = 4 – 53 = -49

𝐴

X₁=𝛥𝑋₁ =

28 7

𝐴

=4

7

X₂= 𝛥𝑋₂ = − 7 = -1

X₃=−

49 7

= -7

Método de Gauss Yordan

2 −5 1 6 2 −5 1 6 2 −5 1 6 A= [−1 4 −1 −1] = (2) [−1 4 −1 −1]= (10) [ 0 3 −1 4 ] 2 5 0 3 0 −10 1 3 (-1) (3)0 −10 1 3 2 −5 1 6 = [ 0 3 −1 4 ] 0 0 −7 49 1) 2𝑋 − 5𝑌 + 𝑍 = 6 2) 3𝑌 − 𝑍 = 4 3) −7𝑍 = 49 𝑍= − Z= -7

49 7

2) 3Y-(-7)= 4 3Y= -3 Y= -1

3) 2X-5(-1)-7= 6 2X+5-7=6 2X=8 X= 4