Let X and Y be vectors in R^3 which are non-collinear with the origin,and let Z be a vector in R^3 that does not lie on
问题描述：
Let X and Y be vectors in R^3 which are non-collinear with the origin,and let Z be a vector in R^3 that does not lie on the plane spanned by X and Y.Then it is possible to express any other vector V in R^3 as a linear combination of X,Y,and Z.
答
因为X与Y线性无关,且Z不能由X与Y线性表示,故X,Y,Z线性无关,它们构成R3中的极大无关组,从而可以表示R3中任意一个向量.