3) Dadas las matrices 1 2 6

2 1 0

2 1 6

k

A k y B

k

−   
   

= − =   
   − −   



Determinar los valores k , para que el sistema .A X B= admita solución única, infinitas soluciones y no admita

solución.

Dado el sistema de ecuaciones

( ) ( ) ( )2

2 2 2

2 2

1 2 1 2
2 1 1 2

2 1 2 1 1 2 2 1 2 2 4
1 2 2 1

2 1 2 1

2 2 2 8 3 3 6

3 3 6 0 2 0 1 2

k k
k k

A k A k k k k k k
k k

k k

k k k k k k

k k k k k k

− − 
− − 

= − → = − = − − = − − − + − − =  − − − − 

− − − − − + = − − +

− − + = → + − = → =  = −




[object Object]
[object Object]
The question is related to linear algebra
The question provides a system of equations to be solved
The question asks to determine the values of k for which the system of equations has a unique solution, infinite solutions, and no solution
The question is related to matrices
a) I, II, and IV are correct.
b) II, III, and IV are correct.
c) I, III, and IV are correct.
d) All afirmacoes are correct.