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Guided Proof Prove that a nonempty subset of a finite set of linearly independent vectors is linearly independent.
Getting Started: You need to show that a subset of a linearly independent set of vectors cannot be linearly dependent.
(i) Assume
(ii) If
(iii) Use this fact to derive a contradiction and conclude that
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Elementary Linear Algebra (MindTap Course List)
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- Proof Let S={u,v} be a linearly independent set. Prove that the set {u+v,uv} is linearly independent.arrow_forwardLinear Combinations In Exercises 1-4, write each vector as a linear combination of the vectors in Sif possible. S={(1,2,2),(2,1,1)} (a) z=(4,3,3) (b) v=(2,6,6) (c) w=(1,22,22) (d) u=(1,5,5)arrow_forward
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