If the subset $\{ v_1,\ldots ,v_k\}$ is a linearly independent subspace of a vector space, for all nonzero vectors $v$ in that vector space, is the set $\{v+v_1,\ldots,v+v_k \}$ also linearly independent?
2026-04-11 21:54:46.1775944486
Is this set linearly independent?
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Consider $\vec{v} = -\vec{v}_1$. It won't be independent