I have no idea where to go with this.
Show that if x1,...,xn are independent vectors in an inner product space, and y≠ 0 is such that y is orthogonal to xi for each i, then y is not a linear combination of x1,...,xn (i.e., is not in the subspace spanned by x1,...,xn )
I know that the x's being independent means that a1x1 + a2x2+...+anxn = 0 iff a1=a2=...=an=0
and that <y,xi> = 0 for each i
And i know that we have to show by the contrapositive that y ≠ a linear combination of the x's so we assume
y = b1x1 + ... + bnxn
I just dont know where to go from here.