Sistemas, matrices y determinantes
Presentation
•
Education
•
1st Grade
•
Practice Problem
•
Hard
Luis Sebastián
Used 6+ times
FREE Resource
0 Slides • 10 Questions
1
Multiple Choice
El determinante de una matriz cuadrada es nulo si y solo si:
No tiene inversa.
Hay una fila idéntica a una columna.
Coincide con su traspuesta.
El rango es nulo.
2
Multiple Choice
Sea A una matriz cuadrada de orden 3 tal que ∣A∣=5 , entonces, se verifica:
∣2A∣ −1 =1/ 10
∣2A∣=10
∣2A∣=20
∣2A∣=40
3
Multiple Choice
Si AX+B=XC+D , entonces:
No es posible despejar X .
X=(A−C) −1 (D−B) , si ∣A−C∣≠0
X=(−B+D)(A−C) −1 , si ∣A−C∣≠0
4
Multiple Choice
Sea A∈Mmxn, se verifica:
AAt =At A
AAt es antisimétrica.
AAt es simétrica.
5
Multiple Choice
Sea A∈Mn(R) ortogonal y simétrica. Se verifica:
∣A∣=1
A=A −1
A+A t =I
(I es la matriz unidad )
∣A∣=-1
6
Multiple Choice
Sean A y A* las matrices de coeficientes y ampliada, respectivamente, del sistema incompatible AX=K. Entonces:
rango(A) < rango (A*)
rango(A) = rango (A*)
rango(A) > rango (A*)
rango(A) = rango (A*)
7
Multiple Choice
Sean A y B matrices cuadradas. Podemos afirmar:
rango(A·B) = rango(B·A).
A·B = B·A.
Traza(A·B) = Traza(B·A).
rango(A·B) = rango(A).rango(B).
8
Multiple Choice
Sea el sistema AX=B con A matriz cuadrada regular:
X=A/B
X=A −1 B
X=BA −1
X=B −1 A
9
Multiple Choice
El determinante de la matriz A=(1 0 −2 )(2 1 2)t es:
no existe el determinante de A
-2
0
2
10
Multiple Choice
Sean A y B matrices cuadradas de orden n≠1 , se verifica:
∣3A∣=3∣A∣
∣AB∣=∣A∣∣B∣
∣AB∣=∣A∣+∣B∣
∣A/B∣=∣A∣/∣B∣
El determinante de una matriz cuadrada es nulo si y solo si:
No tiene inversa.
Hay una fila idéntica a una columna.
Coincide con su traspuesta.
El rango es nulo.
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