- #1
jimmycricket
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Homework Statement
Let [itex]v_1,...,v_k[/itex] be vectors in a vector space [itex]V[/itex]. If [itex]v_1,...,v_k[/itex] span [itex]V[/itex] and after removing any of the vectors the remaining [itex]k-1[/itex] vectors do not span [itex]V[/itex] then [itex]v_1,...,v_k[/itex] is a basis of [itex]V[/itex]?
Homework Equations
The Attempt at a Solution
If [itex]v_1,...,v_k[/itex] span [itex]V[/itex] but [itex]v_1,...,v_{k-1}[/itex] do not then [itex]v_1,...,v_k[/itex] are linearly independent.
If [itex]v_1,...,v_k[/itex] span [itex]V[/itex] and are linearly independent the [itex]v_1,...,v_k[/itex] is a basis of [itex]V[/itex]
Is this reasoning correct?