Regard an n x n matrix as a point in the -fold product Rn x . x

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Regard an n x n matrix as a point in the -fold product Rn x . x Rn by considering each row as a member of Rn..
a. Prove that det : Rn x . x Rn → Rn is differentiable and
b. If aij : R →R are differentiable and f(t) = det (aij(t)), , show that

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Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

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Question Posted: Sep 30, 2009 04:55 AM

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Regard an n x n matrix as a point in the -fold product Rn x . x

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This is an immediate consequence of Problem 214 b and the multi linearity of the determinant f...View the full answer

Linear Algebra with Applications

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