Hi,

problem:Suppose that x and y are vectors and M is a subspace in a vector space V;

let K be the subspace spanned by M and x, and let K be the subspace spanned by M and y.

Prove that if y is in K but not in M, then x is in K.

attempt:So, K is the set of all linear combinations of elements in M and the vector y.

K is also the set of all linear combination of elements in M and the vector x.

This definition of K makes me think that x is always in K.

What am I missing here?

Thanks!