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Matriz y Gauss: repaso clave

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Matriz y Gauss: repaso clave

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Quiz de matrices y métodos de resolución

Created by

Verónica Iñiguez
Verónica Iñiguez
Argentina

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Matriz y Gauss: repaso clave
 

Matriz y Gauss: repaso claveOnline version

Quiz de matrices y métodos de resolución

by Verónica Iñiguez
1

Qué indica que una matriz tiene determinante igual a cero?

2

Si una matriz cuadrada A tiene determinante distinto de cero, ¿qué se puede afirmar de A?

3

Qué representa la matriz aumentada en Gauss para un sistema de ecuaciones no homogeneo?

4

Qué se busca al aplicar el método de Gauss?

5

Qué propiedad tiene la matriz identidad I?

6

Si una matriz A es antisimétrica (A^T = -A), ¿qué puede decirse de su determinante para tamaño impar?

7

Qué resultado se obtiene al multiplicar dos matrices identidad I por cualquier matriz A?

8

En un sistema lineal, ¿qué implica que el determinante de la matriz de coeficientes sea cero?

9

Si se dice que la matriz A es invertible, ¿qué afirmación es correcta?

10

Qué describe la operación de Gauss para el sistema dado x+y+z=1, 2x+y−z=−2, 3x−2y+3z=0?

Explicación

Un determinante nulo implica que el sistema no tiene una única solución.

Un det(A)≠0 implica que A tiene inversa.

Para Gauss, se usa la matriz aumentada [A|b].

Gauss facilita la resolución, no busca directamente el determinante.

I tiene 1 en la diagonal, 0 fuera; su determinante es 1.

Las matrices antisimétricas de tamaño impar tienen determinante 0.

I·A = A y A·I = A.

Det(A)=0 indica no única solución.

La inversa existe si det(A)≠0 y AA^-1=I.

El primer paso típico es definir la matriz aumentada para aplicar Gauss.

 
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