Linearly independent & dependent vectors : Linear Algebra : B.Sc.Mathematics

For a video explanation, click here 👉 https://youtu.be/b0KvzStFHAc

 Linearly Independent Vectors : 

      Let 𝜶1, 𝜶2, … , 𝜶n be any n vectors in a vector space V ( F ). Then the 

    vectors 𝜶1, 𝜶2, … , 𝜶n are  called Linearly Independent vectors , if there exists 

     Scalars a1, a2, … , an  such that a1 𝜶1+ a2 𝜶2+ … + an 𝜶n = 0 implies a1= a2= … = an = 0.


   Linearly Dependent Vectors : 

      Let 𝜶1, 𝜶2, … , 𝜶n be any n vectors in a vector space V ( F ). Then the 

    vectors 𝜶1, 𝜶2,… , 𝜶n are  called Linearly Dependent vectors , if there exists scalars 

    a1, a2, … , an  not all zero such that  a1 𝜶1+ a2 𝜶2+ … + an 𝜶n = 0 

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