i, determine whether the given set S of vectors is closed under addition and closed under...

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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 set of scalars to be the set of all real numbers. 3. The set S := {A € M₂ (R): A is upper or lower triangular}. 5. The set S = {ao + a₁x + a₂x² : ao + a₁ + a₂ = = 1}. 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 € M₂ (R): A is upper or lower triangular}. 5. The set S = {ao + a₁x + a₂x² : ao + a₁ + a₂ = = 1}.

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