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https://texercises.com/exercise/determinant-function/
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Exercise:
We have seen that if D is n-linear and alternating then DA_sigmatextsgnsigma Asigma Asigma ... Ansigma nDepsilon_sigma epsilon_sigma ...epsilon_sigma n But Depsilon_sigma epsilon_sigma ... epsilon_sigma ntextsgnsigma Depsilon_...epsilon_n textsgnsigma DI forall ngeq there exists a unique determinant funciton M_ntimes nKlongrightarrow K. We will denote it by det. It is given by the formula textdetA_sigmatextsgnsigma Asigma Asigma ... Ansigma n

Solution:
Proof. Follows immediately from . Indeed if D is a determinant function then DI and we obtain from that DA_sigma textsgnsigma Asigma Asigma ... Ansigma n.
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Exercise:
We have seen that if D is n-linear and alternating then DA_sigmatextsgnsigma Asigma Asigma ... Ansigma nDepsilon_sigma epsilon_sigma ...epsilon_sigma n But Depsilon_sigma epsilon_sigma ... epsilon_sigma ntextsgnsigma Depsilon_...epsilon_n textsgnsigma DI forall ngeq there exists a unique determinant funciton M_ntimes nKlongrightarrow K. We will denote it by det. It is given by the formula textdetA_sigmatextsgnsigma Asigma Asigma ... Ansigma n

Solution:
Proof. Follows immediately from . Indeed if D is a determinant function then DI and we obtain from that DA_sigma textsgnsigma Asigma Asigma ... Ansigma n.
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determinant, eth, fs23, lineare algebra, proof
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ENG (English)
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Proof
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