Let V be a vector space over the field of real numbers, and let v1,v2 7 and v3 be vectors in V. Suppose v1 and v2 are linearly independent, and v3 is not a scalar multiple of v1 or v2. Can we conclude that v1,v2 and v 3 are linearly independent? Justify your answer.

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05-06-2024
Mathematics

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Let V be a vector space over the field of real numbers, and let v1,v2 7 and v3 be vectors in V. Suppose v1 and v2 are linearly independent, and v3 is not a scalar multiple of v1 or v2. Can we conclude that v1,v2 and v 3 are linearly independent? Justify your answer.

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Let V be a vector space over the field of real numbers, and let v1,v2 7 and v3 be vectors in V. Suppose v1 and v2 are linearly independent, and v3 is not a scalar multiple of v1 or v2. Can we conclude that v1,v2 and v 3 are linearly independent? Justify your answer.

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