Determine why the set S is not a subspace of R³. 1 (8) S= OS is empty O S is not a subset of R3 O | 5x₁ +4x2 − 2x3 = 0 and ₁ ≥ 0, x2 ≥ 0, x3 ≥ 0, 1, 2, 3 € R S is not closed under addition S is not closed under scalar multiplication

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A: Open Sets: The sets in τ are called the open sets of the topological space X, τ. Subspace Topology:…

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A: closure under adiition is clearly satisfied that is a+b=abalso commutative under addition…

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Q: 1 = { x:= = < |x|<1} am an 1. Consider the set Y=[-1,1] as a subspace of R. Is A=< open set in Y? Is…

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Q: 2а + b - Зс 4а — 2b + 5с (а) S %— E R* : a, b, c ER a а +b+c a X1 X2 (b) S = ER: 2x + х2 — 7хз + 8х4…

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A: False

Q: (f) What is span(q, r)? (g) What is span(q, r, s)?

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Q: 7. Show that the set Z of integers is NOT a vector space.

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Q: Let W = a [] b where -6a²-8b²-5 c²=0 C be a subset of R³. Choose the correct statement about W. O W…

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Q: If M is linear subspace of hilbert space H then M is clos

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