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If v1 and v2 are linearly independent vectors in vector space V, and u1, u2, and...

If v1 and v2 are linearly independent vectors in vector space V, and u1, u2, and u3 are each a linear combination of them, prove that {u1, u2, u3} is linearly dependent.

Do NOT use the theorem which states, " If S = { v 1 , v 2 , . . . , v n } is a basis for a vector space V, then every set containing
more than n vectors in V is linearly dependent."

Prove without using the above theorem.

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