Consider a plane P in [itex]ℝ^{3}[/itex]. Is it necessarily the case that any vector outside this plane cannot be expressed as a linear combination of finitely many vectors on this plane?(adsbygoogle = window.adsbygoogle || []).push({});

I would think yes; if you tried to parametrize the plane P with two parameters, could we somehow show that there are no values of the parameters for which the linear combination of the vectors on the plane equals the vector outside the plane?

But I need an expert's opinion on this.

BiP

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# Linear Independence: Is this true?

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