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Publish On: 2019-04-10

Guy white

Total Post: 819

Question: Describe linear independence of vectors

Reply On: 2013-10-05

Mjay Jollay

Total Post: 0

ANS: Describe linear independence of vectors

Let V(F) be a vector space.

A set of a vectors 𝛼1, 𝛼2, 𝛼3, …, 𝛼n of the vector space V is said to be linearly independent if every relation of the form

a1 𝛼1 + a2 𝛼2 + a3 𝛼3 + … + an 𝛼n = 0,

where a1, a2, a3, …., an F.

a1 = a2 = a3 …. = an = 0

i.e. a1 = 0 for each 1 ≤ i ≤ n, ai F.

any infinite set of vectors of V is said to be linearly independent if its every finite subset is linearly independent, otherwise it is linearly dependent.
 

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