# How does Gaussian elimination work? [closed]

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?

• 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 – Wrench 2 days ago