let A = (((0 1 1)),((1 0 1)) )
(1 1 0 )
1) calculate p_c (A) the caracteristic
polunom of A
2) calculate A^n with n integr natural
3) calcypulate e^(tA) t∈ R
E id k vectorial space and f∈L(E)
1)prove that if f is nilpotent with indice
p≥1 ,I −f is bijective and
(I−f)^(−1) =Σ_(i=0) ^(p−1) f^i
2)let E=R_n [x] and f∈L(E) /
f(p) =p−p^′ prove that f is inversible
and find f^(−1) .
let f(x) = e^(−x^2 )
1) prove that f^((n)) (x)=p_n (x)e^(−x^2 ) with p_n is a polynom
2) find a relation of recurrence between the p_n
3) calculate p_1 ,p_2 ,p_3 ,p_4