Let n > 1 and let D be an alternating (n- 1)– linear function on (n 1) x (n– 1)matrices over K. For each j, 1

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Answered: matrices over K. For each j, 1

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matrices over K. For each j, 1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 34E

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Question

Let n > 1 and let D be an alternating (n- 1)– linear function on (n 1) x (n– 1)
matrices over K. For each j, 1 <j<n, the function E; defined by
E;(A) =
E (-1) i +iA¡D#(A)
(1)
i= 1
is an alternating n- linear function on n x n matrices A. If D is a determi nant function, so is each E;.

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