please solve all question.Its an humble request.Functional analysis

Q1.(i) Let || . |1, || . |/2 be two norms on a vector space X and let a, b > 0) such that allx| | |x|las blx], for all x E X. Let {x,} be a Cauchy sequence in (X, | | . |1). Prove that {r,} is also a Cauchy sequence in (X, II . |12). Q1(ii) Let X =R'. Define |all = [ vai| + vz2] ], = = (21, x2) ER'. Prove that || . || does not define a norm on X =R-. Q2(i) Let X= (X, || . Ilx) and Y = (Y, | | . |ly) be normed spaces and TE BL(X, Y). If there is a M > 0 such that ITally 2 M. llllx for all r E X, Show that (i) T-1 : Y - X exists (ii) Also THE BL(X, Y)