Let V be a finite dimensional vector space over a field F with basis ß = {v₁, ..., Vn}, let TEL(V, V). Prove that the following are equivalent: B (a) The matrix [7] is upper triangular. (b) T(v₂) € span (v₁, ..., v;) for all i = 1,..., n. (c) span(v₁,..., v₁) is T-invariant for all i = 1,..., n.