Let the set {v1, v2, v3} be linearly dependent. Prove that {v1, v1+v2, V3} is also linearly dependent. Your help would be greatly appreciated. thank you!
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the Given two vector set are equavalent, thus if the second set is linear independent, then the first set is also linear independent.
following up Shanks words, let's use but is a linear independent set, thus and so is a linear independent set.
Originally Posted by Krizalid following up Shanks words, let's use but is a linear independent set, thus and so is a linear independent set. i think he's trying to prove that the system is linearly dependent. non ?
no, he's trying to prove that the second set is linearly dependent.
the system is linearly dependent if there's some scalars and not all zeros such that, . which give us, setting and since the system is linearly dependent,the scalars aren't all zeros,therefore the system is linearly dependent.
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