Practice question · True or false
A set of three vectors in three-dimensional space in which no vector is a scalar multiple of any other must be linearly independent.
Hints
- Try to build three vectors that all lie in one plane through the origin without any two being parallel.
- Take two vectors and their sum.
Show the answer
False
Why
False. (1,0,0), (0,1,0) and (1,1,0) contain no parallel pair yet are dependent, because the third is the sum of the first two, all three lie in one plane. Dependence is about the whole set, not about pairs.
Practise Linear Independence
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More questions on Linear Independence
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