let A = (((0 m m^2 )),(((1/m) 0 m)) )
((1/m^2 ) (1/m) 0 )
A ∈ M_3 (R) and m not 0
1) find relation betwen I_3 , A and A^2
2) is A inversible .determine A^(−1) in case of exist
3) find the propers values of A.
let p ∈K_n [x] snd A and H two rlements of K[x]
1) prove that p(A(x)+H(x))=Σ_(k=0) ^n ((p^((k)) (A(x)))/(k!)).(H(x))^k
2)find the condition that p(A(x)+H(x))is
divided by H(x)≠0
3) if p(x)≠c prove that p(p(x))−x is divided
by p(x)−x.
Three prizes are awarded each for
getting more than 80%marks,
98% attendance and good
behaviour in the college.In how
many ways the prozes can be
awarded if 15 student of the college
are eligible for the three prizes?