Ian Chen asked in 科學數學 · 6 years ago


1. let V be a two dimensional vector space over R and let T:V -> V be a linear transformation satisfying the identity T^2=T-2*id v show that for any nonzero vector v ? Vthe set ?={v, T(v)} is a basis for V.2.let Vbe a vector space over a field F with dual V*. for any subset S of V define the set E(S)={f?V*l ker(f) ? S} ?V*. thus E(?)=E(0)=V (1)prove that E(S)is a subspace of V*for any S ?V(2)suppose u1,u2,...,up,up+1,..,un is a basis for V for some 1?p<n and let U={u1,u2,...,up} prove that set {u*p+1,u*p+2,...,u*n} is a basis for E(U)

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