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Se da matricea A= [tex] \left[\begin{array}{ccc}1&a&1\\a&1&b\\1&b&1\end{array}\right] [/tex]
Aratati ca daca a≠b , rang A = 2.


Răspuns :

Luam minorul:

1 a
a 1
Calculam det de minor
det=1*a+a*1=2a
daca a diferit de 0 => rang A <=2
det matrice =1*1*1+a*b**1+a*b*1-1*1*1-b*b*1-a*a*1=1+ab+ab-1-b^2-a^2=2ab-b^2-a^2
daca a diferit de b => det=0=> rang A=2