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For example, a matrix denoted by $3$ linear equations that are the linear combination of $3$ elements which come from a subset of a vector space. My question is that could the above 3 linear combination spans the $3$ elements?

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  • $\begingroup$ Sure, for example the real vector space R3 has {(1, 0, 0), (0, 1, 0), (0, 0, 1)} as a spanning set, called the canonical basis (which can be written as the identity matrix). en.wikipedia.org/wiki/Linear_span $\endgroup$ – Wrench 2 days ago

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