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If the set is given how can we show basis of that set?

For example:
Show that the set {(1,0,-1),(1,1,1),(1,2,4)}is a basis for R^3.
6 years ago

SAGAR SINGH - IIT DELHI
879 Points

Dear student,

I guess the first thing to remember is the definition of a basis.   A basis is a linearly independent set of vectors that "span" a space.
In other words, for a set of vectors to form a basis, you have to be able to express any ordered triple (x,y,z) in R^3 as a linear
combination of those vectors, and you can't be able to express a vector in the set as a combination of other vectors in the set.

Sagar Singh
6 years ago
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