Lect8 - Chapter 1 Matrices and Systems of Equations Math1111 Elementary Matrices Properties Let E be an elementary matrix Observation 1 Premultiply by E

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

• Notes
• 18

This preview shows page 1 - 6 out of 18 pages.

Chapter 1. Matrices and Systems of EquationsMath1111Elementary MatricesPropertiesLetEbe an elementary matrix.Observation1Premultiply byE:En×nAn×rperforms row operations onA2Postmultiply byE:Bn×rEn×nperforms column operations onB
Chapter 1. Matrices and Systems of EquationsMath1111Elementary MatricesPropertiesLetEbe an elementary matrix.Observation1Premultiply byE:En×nAn×rperforms row operations onA2Postmultiply byE:Bn×rEn×nperforms column operations onBTheorem1.4.1LetEbe an elementary matrix. Then(a)Eis nonsingular and(b)E-1is an elementary matrix of the same type.
Chapter 1. Matrices and Systems of EquationsMath1111Elementary MatricesProof of TheoremProof.Type I:E=Ii-1011...110In-j
Chapter 1. Matrices and Systems of EquationsMath1111Elementary MatricesProof of TheoremProof.Type I:E=Ii-1011...110In-jClaim:EE=I.
Chapter 1. Matrices and Systems of EquationsMath1111Elementary MatricesProof of TheoremProof.