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Cramer 2x2: Sistema y Determinantes

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Cramer 2x2: Sistema y Determinantes

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Quiz sobre Cramer para sistemas 2x2

Created by

Pierina Vargas
Pierina Vargas
Ecuador

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Cramer 2x2: Sistema y Determinantes
 

Cramer 2x2: Sistema y DeterminantesOnline version

Quiz sobre Cramer para sistemas 2x2

by Pierina Vargas
1

Para el sistema a11 x + a12 y = b1, a21 x + a22 y = b2, cuál es la condición para aplicar Cramer?

2

Si Δ ≠ 0, ¿cómo se obtiene x usando Cramer?

3

Qué representa Δx en Cramer para 2x2?

4

¿Qué ocurre si Δ = 0 y el sistema es compatible?

5

¿Qué ocurre si Δ = 0 y el sistema es incompatible?

6

¿Cómo se llama la solución única cuando Δ ≠ 0?

7

¿Qué representa Δy en Cramer para 2x2?

8

En un sistema 2x2, si a11=2, a12=1, a21=5, a22=3, b1=4, b2=1, ¿Δ?

9

Con Δ ≠ 0 y Δx = 2, Δ = 1, ¿solución x es?

10

Si Δ ≠ 0 y Δy = -3, Δ = 2, ¿solución y?

Explicación

Cramer requiere que el determinante Δ = a11*a22 - a12*a21 sea distinto de cero.

x = Δx/Δ, donde Δx es el determinante al colocar b1, b2 en la columna de x.

Δx se obtiene sustituyendo la columna de coeficientes x por el vector de constantes.

Con Δ=0 puede haber infinitas soluciones o ninguna, según la compatibilidad.

Si Δ=0 y no hay solución, el sistema es incompatible.

Con Δ ≠ 0, el sistema tiene una solución única.

Δy se obtiene sustituyendo la columna de coeficientes y colocando b1, b2 en la segunda columna.

Δ = 2*3 - 1*5 = 6 - 5 = 1. Pero esto parece inconsistente con los números dados; el ejemplo correcto debe recalc. Ajuste: Δ = 2*3 - 1*5 = 1.

x = Δx/Δ = 2/1 = 2.

y = Δy/Δ = -3/2 = -1.5.

 
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