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Math Help - dimension of vector space

  1. #1
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    dimension of vector space

    Let E,F,K be fields such that F \subset E \subset K. Prove that if A=\{a_1,...,a_n\} is a basis for K over E and B=\{b_1,...b_m\} is a basis for E over F, then C=\{a_ib_j, 1 \leq i \leq n, 1 \leq j \leq m\} is a basis for K over F. Conclude that if \dim_E(K) and \dim_F(E) are finite, then \dim_F(K)=\dim_E(K)\dim_F(E).

    I know how to do the proof, but I'm not sure how to conclude that \dim_F(K)=\dim_E(K)\dim_F(E). Some help please.
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  2. #2
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    \dim_E(K)=n,\dim_F(E)=m,\dim_F(K)=n*m,\longrightar  row \dim_F(K)=\dim_E(K)\dim_F(E)\ ?<br />
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