Question: A square matrix A of size n is upper triangular if [A]ij = 0 whenever i > j. Let UTn be the set of all

A square matrix A of size n is upper triangular if [A]ij = 0 whenever i > j. Let UTn be the set of all upper triangular matrices of size n. Prove that UTn is a subspace of the vector space of all square matrices of size n, Mnn.

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