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.

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
AskIITians Expert-IIT DELHI