since need to show direct sum that I have to show v= M+NQuote:

Suppose x1,...., xn (where n>= 2) is a basis of a vector space V. Choose r in {1,....,n-1} and define

M= Span{x1,...,xr},

N= Span{xr+1,....xn}

show that V = M (direct sum) N

and the intersection of M, N is {0}.

But I don't know how to show that the intersection of M, N is {0}.

Plx help