Let's say I have some finite subset of vectors in, lets say, [itex] ℝ^{5} [/itex]. If my set has five linearly independent vectors, they necessarily form a basis for [itex] ℝ^{5} [/itex].(adsbygoogle = window.adsbygoogle || []).push({});

If I have more than 5 vectors, they are linearly dependent. If I have less than 5 vectors, they span only a subspace of [itex] ℝ^{5} [/itex] not equal to [itex] ℝ^{5} [/itex].

My question:

How can I actually compute the span of the vectors I am given? Obviously it is going to be some subspace of [itex] ℝ^{5} [/itex]. But how can I find an explicit representation of that subspace? How can I compute the dimension of that subspace?

Thanks!

BiP

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# How exactly do you compute the span?

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