Consider the set of all those vectors in3 each of whose coor

Consider the set of all those vectors in^3 each of whose coordinates is either 0 or 1; how many different bases does this set contain?

e^2=2-space =set of all ordered pairs(x1, x2) of real numbers.

Where,e1=(1,0);e2=(0,1)

e1, e2 from a basis of R^2

Let,(x1, x2)=v€R^2

V=e1x1+e2x2

R^2 is spanned by e1, e2

Now, we prove that e1, e2 are linearky independent

C1e1+c2e2=(0,0)

C1=c2=0

So, e1, e2 are linealy independent

Hence, e1, e2 forms a basis of R^2

THE PROOF IS COMPLETE

DIMENSION=2