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Question

If v1andv2 are 2 vectors, then c1v1+c2v2.v2 is the linear combination of these 2 vectors where c1,c2`εR.

A
True
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B
False
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Solution

The correct option is B False
Linear combination of n vectors as discussed is the sum of all vectors each scaled up or down by some scalar. Let’s say we have n vectors v1,v2........vn, their linear combination will be c1v1+c2v2+....cnvn where c1c2.....cn are all scalars (any real numbers). Here in each of the n terms each of the vector is multiplied by a scalar only and not by any other vector. Hence the word linear combination is used. So c1v1+c2v2 will be the linear combination for vectors v1andv2 and not c1v1+c2v2.v2

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