An algebra problem by Hobart Pao

Algebra Level pending

Does there exist a vector a ⃗ ∈ R n \vec{a} \in \mathbb{R}^n such that every vector b ⃗ ∈ R n \vec{b} \in \mathbb{R}^n is linearly dependent to a ⃗ \vec{a} ?

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Hobart Pao by Hobart Pao , 23, USA

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1 solution

Hobart Pao
May 15, 2017

This a ⃗ \vec{a} is 0 ⃗ \vec{0} , because you can take any linear combination of vectors and make the trivial relation, meaning 0 ⃗ = ∑ k = 1 n c k v ⃗ k \vec{0} = \displaystyle \sum_{k = 1}^n c_k \vec{v}_k , where v ⃗ k ∈ R n \vec{v}_k \in \mathbb{R}^n .

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