Mathematics, 24.09.2020 16:01 pablohc200021
Consider the following sets of vectors. Determine whether the sets are subspaces of R 3. If a set is a not a subspace, explain why. If a set is a subspace, give a basis and its dimension.
A) S is the set of vectors of the form (a, 1, 3).
B) S is the set of vectors of the form (a, 0, 0).
C) S is the set of vectors of the form (2a, b, a 1)
D) S is the set of vectors of the form (2a, b 1, a).
E) S is the set of vectors of the form (a 2 , b2 , a2 b 2 ).
Answers: 1
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Given: ae ≅ ce ; de ≅ be prove: abcd is a parallelogram. we have that ab || dc. by a similar argument used to prove that △aeb ≅ △ced, we can show that △ ≅ △ceb by. so, ∠cad ≅ ∠ by cpctc. therefore, ad || bc by the converse of the theorem. since both pair of opposite sides are parallel, quadrilateral abcd is a parallelogram.
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