Homepage › Solution manuals › Gilbert Strang › Introduction to Linear Algebra › Exercise 2.7.3

Introduction to Linear Algebra

Exercise 2.7.3

Answers

(a): ${({(AB)}^{- 1})}^{T} = {(B^{- 1} A^{- 1})}^{T} = {(A^{- 1})}^{T} {(B^{- 1})}^{T} .$ This is also ${(A^{T})}^{- 1} {(B^{T})}^{- 1}$ .
(b): If $U$ is upper triangular, so is $U^{- 1} :$ then ${(U^{- 1})}^{T}$ is lower triangular.

mathchakra

2021-12-20 21:25

Comments