Theorem • V has a basis v_1,…,v_n, and another basis w_1,…,w_n • Let T be a linear transformation V→V • Define the following matrices ○ A≔matrix(T,v_i ) ○ B≔matrix(T,w_i ) ○ C≔∀i∈{1,…,n}, C(w_i )=v_i • Then B=C^(−1) AC Question • Given ○ T:R3→R3 ○ f(T)=(2−λ)^2 (3−λ) ○ dim(Null(T−2I))=1 • Find T ○ T=[■8(2&1&0@∗&2&0@0&∗&3) ○ For λ=2 ○ Tv=2v ○ ⇒v=k[█(1@0@0)]
