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I would appriciate your help with the question below :

V is a vector space with inner product.

A = {a1,...,ak}   B = {b1,...,bk}  such that :

 = {1 , i = j
            {0 , i != j         for  1 <= i,j <= k

I want to know if spB = (spA)⊥

(⊥ is a sign for euclidean vector space , such that every vector in the subspace is orthogonal to every vector in the complement)

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    Certainly not. After all $\langle a_1,b_1\rangle=1$ and not $=0$ – 2017-01-13
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    How can that be possibe if for example $\;\langle a_1,b_1\rangle=1\neq0\;$ and thus $\;b_1\rlap{\;\,/}\perp a_1\;$ ?! – 2017-01-13

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