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is it always possible? (I don't know the basic concept)

My question is same as "If n vectors are linearly independent, is their span R^n" this question??

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  • $\begingroup$ Can you please phrase your question in a more understandable manner? As it is, this does not really make sense. I presume that you wanted to ask ‘If a vector space is of dimension n and I have a set of n vectors that are linearly independent, does that set form a basis for the vector space?’. If that is what you wanted to ask, edit your question accordingly. $\endgroup$
    – Mousedorff
    Commented May 7, 2020 at 10:25

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Yes if the vectors have $n$ coordinates ! It's true ! By the definition of being independent. Find the solution here : If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?

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  • $\begingroup$ thanks, Then, the comment"If the vectors have n coordinates"is not in the question the question is false? $\endgroup$
    – markorzs
    Commented May 7, 2020 at 10:34
  • $\begingroup$ Hum... Yeah but you will figure out quickly. $\endgroup$
    – CechMS
    Commented May 7, 2020 at 15:29
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If you have $n$ linearly independent vectors in $\mathbb R^n$ the span is exactly $\mathbb R^n$ whereas, if you have $n$ linearly independent vectors in some real vector space $V$ then the span of those vectors is linearly isomorphic to $\mathbb R^n$.

In general, in any vector space $V$ over a field $\mathbb F$ span of any $n$-linearly independent vectors form a subspace $\mathbf{isomorphic}$ to $\mathbb F^n$.

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