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 𝛼

a

where a

a

i.e. a

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.

A set of a vectors 𝛼

_{1}, 𝛼_{2}, 𝛼_{3}, …, 𝛼_{n}of the vector space V is said to be linearly independent if every relation of the forma

_{1}𝛼_{1}+ a_{2}𝛼_{2}+ a_{3}𝛼_{3}+ … + a_{n}𝛼_{n}= 0,where a

_{1}, a_{2}, a_{3}, …., a_{n}F.a

_{1}= a_{2}= a_{3}…. = a_{n}= 0i.e. a

_{1}= 0 for each 1 ≤ i ≤ n, a_{i}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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