Suppose we have a set of three vectors S = {V₁, V2, V3} CR². Which one of the following is a true statement? (a) S will be a basis for R2 only if one of the vectors is the zero vector. (b) S will be a basis for R2 if and only if v₁, V2, and v3 are linearly independent. (c) S will be a basis for R2 as long as it is possible to write V3 = C1v1 + c2V2. (d) S cannot be a basis for R² because 3 vectors cannot span R². (e) S cannot be a basis for R2 because 3 vectors cannot be linearly independent in R².

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A: Since, dimension of a vector space is equal to number of elements in basis of vector space.

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A: The vectors v1=7-60, v2=-42-4,  and v3=13-14kform a basis for R3 if and only if k≠?.

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