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Gauss sencillo: juego de matrices

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Gauss sencillo: juego de matrices

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Resolver con eliminación de Gauss

Created by

Pablo Ramos osorio
Pablo Ramos osorio
Guatemala

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Gauss sencillo: juego de matrices
 

Gauss sencillo: juego de matricesOnline version

Resolver con eliminación de Gauss

by Pablo Ramos osorio
1

¿Cuál es el paso inicial típico en la eliminación de Gauss para un sistema lineal?

2

Qué operación está permitida para convertir la matriz en forma escalonada?

3

¿Qué indica un pivote en la eliminación de Gauss?

4

Al terminar Gauss, ¿qué forma debe tener la matriz para lectura de soluciones?

5

¿Qué significa una fila con todos ceros en una matriz aumentada?

6

Qué condición debe cumplir el pivote en cada paso para avanzar?

7

¿Qué operación afecta una fila para eliminar una variable?

8

¿Qué se obtiene al aplicar Gauss sin normalizar pivotes a 1?

9

¿Qué indica una contradictoria en Gauss, como fila [0 0 | b] con b ≠ 0?

10

En un sistema 2x2, con matriz aumentada [ [1,2|5], [0,0|3] ], ¿hay solución?

Explicación

Se empieza con la matriz aumentada y se escoge un pivote en la primera columna.

Permiten intercambiar filas, escalar y sumar múltiplos de filas.

El pivote es un elemento no nulo que guía la eliminación.

Se busca escalonada o RREF para extraer soluciones.

Fila cero en augmented suele indicar dependencia y posibles infinitas soluciones.

Pivote distinto de cero; normalizar puede ayudar.

Se usan filas para eliminar la variable objetivo.

La normalización facilita la lectura de la solución, pero Gauss funciona sin ella.

Una fila 0 … 0 | no nulo implica inconsistencia.

La segunda fila 0 0 | 3 es imposible.

 
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