It's hard to find the proofs of these theorems. Please help me... Thanks!(adsbygoogle = window.adsbygoogle || []).push({});

Theorem 1: Let V be a vector space over GF(q). If dim(V)=k, then V has [tex]\frac{1}{k!}[/tex] [tex]\prod^{k-1}_{i=0}[/tex] (q[tex]^{k}[/tex]-q[tex]^{i}[/tex]) different bases.

Theorem 2: Let S be a subset of F[tex]^{n}_{q}[/tex], then we have dim(<S>)+dim(S[tex]^{\bot}[/tex])=n.

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# Help me with these proofs (vector spaces over finite fields)

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