Suppose {v₁, ..., vr} is linearly independent but does not generate the vector space V. Show there exists a vector Vr+1 such that {V₁,..., Vr, Vr+1} is linearly independent. Hint: Since the set is not generating, there is a vector Vr+1 that is not a linear combination of the vį (i = 1, ..., r). Then show that (v₁,..., Vr+1} is linearly independent.

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A: According to the given information suppose,

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A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

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A: Please check the next step for details

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Q: vector

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A: This question is related to linear algebra (inner product space).

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Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such…

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