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Exercise:
forall ngeq exists at least one determinant function M_ntimes nKlongrightarrow K.

Solution:
Proof. Induction on n. For n M_times Klongrightarrow K amapsto a is a determinant function. For n we have seen that a determinant function. M_times Klongrightarrow K exists. If a determinant function exists for M_n-times n-K then by the previous theorem a determinant function exists also for M_ntimes nK.
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Exercise:
forall ngeq exists at least one determinant function M_ntimes nKlongrightarrow K.

Solution:
Proof. Induction on n. For n M_times Klongrightarrow K amapsto a is a determinant function. For n we have seen that a determinant function. M_times Klongrightarrow K exists. If a determinant function exists for M_n-times n-K then by the previous theorem a determinant function exists also for M_ntimes nK.
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determinant, eth, fs23, lineare algebra, matrices, proof
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(3, default)
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ENG (English)
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Proof
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