Suppose {v,w} is a linearly independent set in the vector space V.Then the set {v,v+w} is also linearly independent.A. TrueB. False
Question
Solution 1
To determine whether the set {v, v+w} is linearly independent, we need to consider the linear combination of its elements.
Let's assume that there exist scalars a and b such that av + b(v+w) = 0, where 0 represents the zero vector in V.
Expanding this equation, we get av + bv + bw = 0.
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