Chapter 2.3 Determinants-Properties

# Then the following are equivalent they are all true

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Unformatted text preview: trix. Then the following are equivalent (they are all true or they are all false). (a) A is invertible. (b) Ax = 0 has only the trivial solution. (c) rref (A) = In . (d) A = E1 E2 . . . Er for some elementary matrices E1 , E2 , . . . , Er . (e) Ax = b has exactly one solution for every n × 1 column vector b. (f) det A = 0. Outline Linearity of the Determinant Determinants and Invertibility Determinants and Products Determinants and Inverses The Determinant of a Product with an Elementary Matrix Theorem If A is an n × n matrix and E is an n × n elementary matrix, then det(EA) = (det E )(de...
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## This note was uploaded on 02/10/2014 for the course MATH 2270 taught by Professor Kenyonj.platt during the Spring '14 term at Snow College.

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