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i, determine whether the given set S of vectors is closed under addition and closed under scalar mul- tiplication. In each case, take the

i, determine whether the given set S of vectors is closed under addition and closed under scalar mul- tiplication. In each case, take the set of scalars to be the set of all real numbers. 3. The set S := {A M (R): A is upper or lower triangular}. 5. The set S = {ao + ax + ax : ao + a + a = = 1}.

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