Question

Suppose that x and y are vectors and M is a subspace in a vector space V
Let H be the subspace spanned by M and x
Let K be the subspace spanned by M and y.
Prove that if y is in H but not in M, then x is in K.
Please, help

Answer 1

H = Span (M +x)
K = Span ( M + y)
case 1: x \(\in M\), y \(\in M\)
case 2: x \(\in M\) , y \(\notin M\)
case 3: x\(\notin M\) , y \(\in M\)
case4: both x , y \(\notin M\)
Is there any else? please, help