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Can anyone help guide me along in this proof?

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- Thread starter zmdeez
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Can anyone help guide me along in this proof?

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matt grime

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matt grime

Science Advisor

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What is the span of a subset? iti s the set of all combinations

[tex]t_1x_1+\ldots t_nx_n[/tex]

for t_i in R (or the underlying field) and x_i in W

so W=span(W) means exactly that all finite combinations of elements of W are in W.

so we are trying to show that

W closed under combining (adding up) two elements of itself if and only if W is closed under combining a finite number of elements of itself.

Obvioulsy one way is simple: if i can add up any number of combinations of elements then i can in particular add up two of them. Conversely...?

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