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We look at the following exciting exercise from the wonderful world of linear algebra: Let V, W be R-vector spaces and f a mapping from V to W., then: f is a linear mapping if and only if the graph of f is a subspace of the direct sum of V and W. linear algebra, vector space, mapping, linear, if and only if, proof, exercise, solution, exam, state exam, uvr, subspace, subvector space, definition, sum, product space, direct, graph