Can a single vector be linearly independent? Is span <1,1,1,0> linearly independent? We have that the only solution to c⋅<1,1,1,0> is c=0, so it is indeed linearly independent? But this is a single vector, does it still hold?

lamesa1Vy

lamesa1Vy

Answered question

2022-11-25

Can a single vector be linearly independent?
Is span   < 1 , 1 , 1 , 0 > linearly independent?
We have that the only solution to c < 1 , 1 , 1 , 0 >, so it is indeed linearly independent? But this is a single vector, does it still hold?

Answer & Explanation

Arturo Hogan

Arturo Hogan

Beginner2022-11-26Added 13 answers

The span of a vector is not a vector, rather the set of linear combinations of that vector and thereby trivially linearly dependent. A vector v 0 itself is always linearly independent since the equation
λ v = 0
only has the solution λ = 0 (where λ is a scalar).

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