Recall the definition of Linear Independence: The set {V1,..., Vn} is linearly independent if, whenever a₁ V₁ + + an Vn = 0, it must be that = an = 0. a₁ = Suppose that {v2, V3} is linearly independent. Briefly describe what is wrong with the following "proof" that {V1, V2, V3} is linearly independent (where V₁ is some nonzero vector): Since (v2, V3} is linearly independent, a2 V2 + a3 V3 = 0. Then, if a₁ V₁ + a2V2 + a3 V3 = 0, we have that a₁ V₁ + 0 = 0 so that a₁ = 0. Therefore, {V1, V2, V3} is linearly independent.

Q: b. Determine the value(s) of b such that the set S = is linearly independent in M

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Q: how that the set S={(1,2,1),(3,1,5),(3,-4,7)}  is linearly dependent where, S⊆V\index{3}(R).

A: Our Claim is to show that Set S is linear dependent in V\index{3}(R).Since we know that if u,v and r…

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Q: ppose S = &v₁₁ ore that T = nearly independ

A: Answer given below.

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A: We can solve this as follows:

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A: To find which of the following is correct for the given sets .

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Q: (c) {(1,−1,2,0), (1,1,2,0), (3,0,0,1)} ℃ Rª 3 2 6 {O·O·O·}- 3 3 (d) 1 2 -2 0 2 CR¹

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