Question 1129644: Prove that if {v1, v2, v3} is a linearly independent set of vectors, then so are {v1, v2}, {v1, v3}, {v2, v3}, {v1}, {v2}, and {v3}.
Will anyone provide me some guideline how to solve this problem, please?
Thank you in advance.
Found 2 solutions by solver91311, rothauserc:
Answer by solver91311(24713)   (Show Source):
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! A set of vectors is linearly independent if no vector in the set is (a) a scalar multiple of another vector in the set or (b) a linear combination of other vectors in the set
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for example, the following row vectors are linearly independent
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v1 = (2, 4, 6)
v2 = (0, 1, 0)
v3 = (0, 0, 1)
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that should get you going
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Note that if we have
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v1 = (1, 2, 3)
v2 = (4, 5, 6)
v3 = (5, 7, 9)
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then (v1, v2, v3) is linearly dependent since v3 is a linear combination of v1 and v2
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