Lect8 - Chapter 1. Matrices and Systems of Equations...

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Unformatted text preview: Chapter 1. Matrices and Systems of Equations Math1111 Elementary Matrices Properties Let E be an elementary matrix. Observation 1 Premultiply by E : E n × n A n × r performs row operations on A 2 Postmultiply by E : B n × r E n × n performs column operations on B Chapter 1. Matrices and Systems of Equations Math1111 Elementary Matrices Properties Let E be an elementary matrix. Observation 1 Premultiply by E : E n × n A n × r performs row operations on A 2 Postmultiply by E : B n × r E n × n performs column operations on B Theorem 1.4.1 Let E be an elementary matrix. Then (a) E is nonsingular and (b) E- 1 is an elementary matrix of the same type. Chapter 1. Matrices and Systems of Equations Math1111 Elementary Matrices Proof of Theorem Proof. Type I: E = I i- 1 1 1 . . . 1 1 I n- j Chapter 1. Matrices and Systems of Equations Math1111 Elementary Matrices Proof of Theorem Proof. Type I: E = I i- 1 1 1 . . . 1 1 I n- j Claim: EE = I . Chapter 1. Matrices and Systems of Equations Math1111 Elementary Matrices Proof of Theorem Proof.Proof....
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Lect8 - Chapter 1. Matrices and Systems of Equations...

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