Is This true or not ? If yes , please provide a proof.
2026-03-29 20:51:49.1774817509
If a set of n vectors are linearly dependant then n-1 vectors of the same set must be linearly independant .
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Not true. Counter-example over the field of reals (or field of rationals, etc.) $S=\left\{\begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix},\begin{bmatrix}10 \\ 20 \\ 30 \end{bmatrix},\begin{bmatrix}100 \\ 200 \\ 300 \end{bmatrix}\right\}$.