Chapter 1.5 Inverses-LinearSystems

A a is invertible b ax 0 has only the trivial

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Unformatted text preview: t. (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. Proof. (e) ⇒ (b): Take b = 0. (b) ⇒ (a): Done. (a) ⇒ (e): If A is invertible, then c = A−1 b and Ac = b. If c is another solution, then c = A−1 Ac = A−1 b = c. Outline Number of Solutions Solving Multiple Systems More Results On the Inverse Example Example Find the solution of the 1 1...
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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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