1° PARCIAL
30/09/22
TEMA 6
1) Hallar las matrices

0 0
1 0
0 1
a
X b
c
 
 

=  
 
 

tales que se verifique que

2 4 0 0 0
0 4 0 0 0
1 0 4 0 0

X
 
 

=  
 
 

.

2 2 2
2
2
0 0 4 0 0
1 0 0 4 0
0 1 1 0 4
0 0 0 0 0
. 1 0 1 0
0 1 0 1
a
Dada X b debemos hallar las matrices que verifican la siguiente condición X
c
Primero debemos hallar la matriz X

a a a
X X X b b
c c
   
   

= =   
   
   

  
  

= = =  
  +    = → =  

2
2
2
2
2 2 2
2
0
0
1
4 2
04 0 0 0 0 4 0 0
0 4 0 0 0 4 0 4 2
1 0 4 1 1 0 4 4 2
0

,
a b b
b c c

Sabemos que

a a
a b b aa
X a b b b b
b c c c c
b c c b

Tenemos entonces dos posibles matrices X

 
 

+ 
 + 

 = → = 


+ = → = −    
    

= → + = → = → =     
    +    = → =   


+ = → = −


[object Object]
[object Object]
[object Object]
The question is related to algebra and matrices
The question asks to find matrices that satisfy a given condition
The question provides a system of equations to be solved
The question is related to the topic of linear algebra
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.