Let V be a finite dimensional vector space over a field F, and let v 1 , , v n be a basis for V Suppose that for each 1 i n, T(v i ) span(v 1 , , v i ) Prove that T is upper triangular Recall that a matrix is upper triangular if every entry below the main diagonal is 0

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Question: Let V be a finite dimensional vector space over a field F, and let = {v 1 , . . . , v n }

Let V be a finite dimensional vector space over a field F, and let = {v₁, . . . , v_n} be a basis for V . Suppose that for each 1 i n, T(v_i) span(v₁, . . . , v_i). Prove that [T] is upper triangular. Recall that a matrix is upper triangular if every entry below the main diagonal is 0.

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